UC-NRLF 


.  APPLETON  &  CO.,  New  York. 


LIBRARY 

OF  THE 

UNIVERSITY  OF  CALIFORNIA. 


Received      t^Jr  .  189  n  . 

Accession  No.  (b  7  J~£/    .    Class  No. 


APPLETOHS'  MATHEMATICAL  SERIES. 


>   A 


PRIMARY    ARITHMETIC 


BT 

G:  P.  QUACKENBOS,  A.  M., 

AUTHOR  OF 

"AN  ENGLISH  GRAMMAR;"  "FIRST  LESSONS  IN  COMPOSITION;"  "ADVANCED 

COURSE  OF  COMPOSITION  AND   RHETORIC;"     UA   NATURAL  PHILOSO- 
PHY;1'   "ILLUSTRATED  SCHOOL   HISTORY   OF  THE   UNITED 
STATES  J  "    "  PRIMARY   HISTORY   OF  THE   UNITED 
STATES  J  "    ETC. 


UPON     THE      BASIS      OP      THE      WORKS      OF 

GEO.  R.  PERKINS,  LL.D. 

^^ 


\ 

N 
D.    APPLETON    AND    COMPANY, 

443    &   445    BKOADWAY. 

1864. 


PREFACE. 


This  little  book,  the  first  of  our  Series  of  Arithmetics,  presup- 
poses no  knowledge  of  numbers  whatever.  It  tries  to  give  a  cor- 
rect idea  of  their  value,  both  absolute  and  relative,  by  treating 
them  concretely  as  well  as  abstractly  from  the  very  outset,  pictorial 
illustrations  being  freely  used  for  that  purpose.  We  have  not 
sought  in  its  pages  to  go/ar,  but  to  go  thoroughly.  It  is  therefore 
i  confined  to  the  four  fundamental  operations,  a  very  brief  view  of 
fractions,  the  most  important  tables  of  moneys,  weights,  and  meas- 
ures, and  easy  exercises  under  them.  These  subjects,  it  is  believed, 
are  so  treated,  as  to  make  the  young  pupil  think  for  himself,  and  to 
lay  the  right  kind  of  foundation  for  a  mathematical  course.  One 
thing  is  taught  at  a  time,  and  great  care  has  been  taken  to  present 
every  thing  in  its  proper  place.  It  will  be  observed  that  through- 
out the  book  slate  exercises  go  hand  in  hand  with  mental  opera- 
tions. In  the  author's  opinion,  they  are  indispensable,  from  the 
first,  for  inspiring  the  beginner  with  that  interest  in  the  subject 
which  is  essential  to  success. 

This  book  imposes  no  labor  on  the  teacher,  in  the  way  of  ex- 
plaining orally,  setting  sums,  &c.  It  is  thought  to  contain  in  itself 
all  that  is  needed.  The  author  would  only  ask  those  who  use  it  to 
be  sure  that  every  lesson  is  thoroughly  mastered,  before  proceed- 
ing to  the  next.  Each  principle  presented,  each  table,  should  be 
perfectly  understood  and  memorized  before  leaving  it,  even  though 
it  be  necessary  to  repeat  the  lesson  again  and  again.  Time  saved 
by  allowing  a  single  lesson  to  pass  unmastered,  will  be  a  tenfold 
loss  in  the  end. 


Entered,  according  to  Act  of  Congress,  in  the  year  1863,  by 

D.  APPLETON  &  CO., 

In  the  Clerk's  Office  of  the  District  Court  of  the  United  States  for  the 
Southern  District  of  New  York. 


PRIMARY  ARITHMETIC. 


LESSON    I. 

Touch  your  head.  How  many  heads 
have  you  ?  ONE. 

Touch  your  eyes.  How  many  eyes 
have  you  ?.  Two. 

Touch  the  joints  of  your  fore-finger. 
How  many  are  there  ?  THREE. 

Touch  the  fingers  of  your  left  hand. 
How  many  are  there  ?  FOUK. 

Touch  the  fingers  and  thumb  of  your 
left  hand.  How  many  do  they  make  ?  FIVE. 

When  we  say  ONE,  TWO,  TTTKEE,  FOUK,  FIVE, 
what  do  we  do  ? 

Answer.  We  count. 

Count  five ;  count  four ;  count  three ;  count 
two. 

What  are  one,  two,  three,  lour,  five,  called? 
Answer.  Numbers. 

Which  is  the  smallest  of  these  numbers  ? 
Which  is  the  greatest  of  these  numbers  ? 


COUNTING. 


LESSON    II. 

Count  the  birds  on 
this  branch.  How 
many  are  there  ?  FIVE. 

If  another  alights 
on  it,  how  many 
will  there  be  ?  Six. 

Ifanotherjoins 
them,  how  many 
will  that  make  ?  SEVEN. 

If  another 
comes,  how 
many  ?  EIGHT. 

One  more 
will  make 

*  how  many  ?  NINE. 
And  one 
more,  how 
many  ?         TEN. 
Count  six ;  count  seven  ;  eight ;  nine ;  ten. 
Which  is  greater,  ten  or  five  ?     Two  or  six  ? 

"What  do  we  use,  to  express  numbers  ? 
Answer.  Ten  characters,  called  Figures. 

Learn  the  names  of  these  ten  figures,  and  how 
to  make  them  neatly  on  your  slate. 

NAUGHT       ONE      TVTO       THREE       FOUR       FIVE        BIX      SEVEN      EIGHT     NINB 


0        /     2 


/ 


I 


COUNTING. NUMERATION. NOTATION. 


Count  these  rabbits.     How  many  are  there  ? 
How  do  we  express  ten  with  figures  ? 
Answer.  By  putting  a  naught  after  a  one  (10). 

Learn  the  numbers,  going  up  from  ten : — 
Eleven      //      Fourteen  /-/     Seventeen 
Twelve     /2      Fifteen      /^     Eighteen 
Thirteen    /J>      Sixteen     /^     Nineteen     /  <? 
Twenty  .     .     .     20 

Eead  these  numbers :  13 ;  7  ;  19  ;  11 ;  9  ;  2  ; 
20  ;  12  ;  5  ;  16  ;  3  ;  10 ;  4  ;  18  ;  6  ;  15  ;  8  ;  17. 

Write  in  figures,  six  ;  ten ;  three  ;  eighteen  ; 
eight ;  twenty ;  two  ;  twelve  ;  fourteen  ;  five. 

What  is  the  reading  of  numbers  called? 
Answer.  Numeration. 

What  is  the  writing  of  numbers  called? 
Answer.  Notation. 


COUNTING. 


LESSON    IV. 

ISTow  we  have  some  marks  in  different  rows. 
Count  those  in  each  row. 

The  number  of  marks  is  given  after  each  row ; 
then  come  the  written  figures  that  represent  this 
number,  then  the  printed  figures. 

I ONE  </  1 

.Two  -22 

THREE  3  3 

, FOUR  ^  4 

FIVE  &  5 

Six  ^6 

SEVEN  y  7  j 

EIGHT  <?  8 

NINE  y  9 

TEN  /^  10 

ELEVEN  //  11 

TWELVE  /^  12 

THIRTEEN  /c?  13 

FOURTEEN  -/•£  14 

| FIFTEEN  ^  15 

||  ....  SIXTEEN  /^  16 

Ml  ....  SEVENTEEN  <//  17 

[111  ...  EIGHTEEN  /<f  18 

|  1  |  |  |  ...  NINETEEN  //  19 

|  |  |  |  |  [  .  .  TWENTY  20  20 

Which  is  greater,  twenty  or  ten  ?     11  or  18  ? 


COUNTING. 


LESSON   V. 


Twenty-seven  27 
Twenty-eight  28 
Twenty-nine  29 


Learn  the  twenties  : — 

Twenty-one  21  Twenty-four  24 
Twenty-two  22  Twenty-five  25 
Twenty-three  23  Twenty-six  26 

In  the  twenties,  which  figure  remains  the 
same,  and  which  does  not  ? 

Answer.  The  left-hand  figure  remains  the 
same — 2.  The  right-hand  figure  changes. 

What  comes  after  29  ?     Answer.  Thirty  (30). 

Learn  the  thirties : — 

Thirty-one       31     Thirty-four  34  Thirty-seven  37 

Thirty-two       32     Thirty-five  35  Thirty-eight  38 

Thirty-three    33     Thirty  six  36  Thirty-nine  39 

What  is  the  left-hand  figure  in  all  the  thirties  ? 
Which  figure  changes  ? 

What  comes' after  39?      Answer.  Forty  (40). 

Learn  the  forties  : — 


Forty-  one 
Forty-two 
Forty-three 

41     Forty-four       44 
42     Forty-five        45 
43     Forty-six         46 
Fifty  ....     5 

Forty-seven     47 
Forty-eight      48 
Forty-nine       49 
0 

Which 
28  or  38? 

is  greater,  fifty  or  forty  ?     49  or  39  ? 
26  or  17?     9  or  15?     15  or  30? 

Count 

from  1  to  50.      Count  from  20  to  1 

backwards 

;  twenty,  nineteen,  eighteen,  &c. 

8                                              COUNTING. 

LESSON    VI. 

Learn  the  numbers,  going  up  from  fifty  :  — 

Fifty                 50 

Sixty-seven      67 

Eighty-four      84 

Fifty-one          51 

Sixty-eight       68 

Eighty-five       85 

Fifty-two          52 

Sixty-nine        69 

Eighty-six        86 

Fifty-three       53 

Seventy            70 

Eighty-seven    87 

Fifty-four         54 

Seventy-one      71 

Eighty-eight     88 

Fifty-five          55 

Seventy-two     72 

Eighty-nine      89 

Fifty-six           56 

Seventy-three  73 

Ninety              90 

Fifty-seven       57 

Seventy-four     74 

Ninety-one       91 

Fifty-eight       58 

Seventy-five      75  1  Ninety-two       92 

Fifty-nine         59 

Seventy-six      76 

Ninety-three     93 

Sixty                60 

Seventy-seven  77 

Ninety-four      94 

Sixty-one          61 

Seventy-eight  78 

Ninety-five       95 

Sixty-two          62  I  Seventy-nine    79 

Ninety-six        96 

Sixty-  three       63    Eighty              80 

Ninety-seven    97 

Sixty-four         64 

Eighty-one       81 

Ninety-eight     98 

Sixty-five          65 

Eighty-two       82- 

Ninety-nine      99 

Sixty-six           66 

Eighty-three    83 

One  hundred  100 

How  many  figures  does  100  contain  ? 

"What  is  the  greatest  number  that  can  be  ex- 

pressed with  two  figures  ?                   Answer.  99. 

What  is  the  greatest  number  that  can  be  ex- 

pressed with  one  figure  ?                       Answer.  9. 

Name  in  order  the  numbers  between  1  and 

100  that  contain  naught. 

Ans.  10,  20,  30,  40,  50,  60,  TO,  80,  90,  100. 

COUNTING. 


LESSON   VII. 


Here  is  a  factory  ten  stories  high.  How  many 
windows  are  there  in  each  story  ? 

Count  the  windows  in  the  two  lowest  stories. 
How  many  do  you  find?  How  many  rows  of 
10  each  make  20  ?  How  many  tens  in  20  ? 

Count  the  windows  in  the  three  lowest  stories. 
How  many  tens  in  thirty  ? 

Add  another  row  of  windows,  and  how  many 
do  you  find  ?  How  many  tens  in  forty  ? 

Count  the  windows  in  the  five  lowest  rows. 
How  many  tens  in  fifty  ? 

How  many  tens  in  60  ?  How  many  tens  in 
70  ?  How  many  tens  in  eighty  ?  How  many 
tens  in  90  ? 

Count  all  the  windows.    How  many  are  there  ?  ! 
How  many  rows  of  10  each  make  100  ?     How 
many  tens  in  one  hundred  ? 


10  UNITS. — TENS. 


LESSON    VIII. 

Learn  this  table  : — 


20  is  2  tens. 
30  is  3  tens. 
40  is  4:  tens. 
50  is  5  tens. 


60  is  6  tens. 
70  is  7  tens. 
80  is  8  tens. 
90  is  9  tens. 


Which  figure  shows  the  number  of  tens  ? 
Answer.  The  second,  or  left-hand  figure. 

What  is  the  second  place  called  ? 
Answer.  The  place  of  tens. 

What  is  the  first,  or  right-hand  place  called? 
Answer.  The  place  of  units. 

Write  down  22.     What  figures  do  you  use  ? 

Have  these  twos  the  same  value  ? 
Answer.  ~No.     The  2  in  the  second  place  is 
ten  times  as  great  as  the  2  in  the  first  place. 

Why  is  this  ? 

Answer.  Because  the  2  in  the  second  place 
denotes  two  tens,  or  twenty  ;  the  2  in  the  first 
place  denotes  two  units,  or  two. 

What,  then,  is  the  effect  of  removing  a  figure 
from  the  first  place  to  the  second  ? 

Answer.  Its  value  is  increased  ten  times ;  20 
is  ten  times  as  great  as  2. 

Write  down  the  numbers  from  1  to  100. 


UNITS. TENS.  11 


LESSON    IX. 

How  do  you  write  six  tens  ? 

Ans.  6^  in  the  second  place  denotes  six  tens. 
As  there  are  no  units,  I  put  a  0  after  it — 60. 

How  do  you  write  six  tens,  one  unit? 

Ans.  6  in  the  second  place  denotes  six  tens  ; 
1  in  the  first  place  denotes  one  unit — 61. 

Head  this  number.  Ans.  Sixty-one. 

How  must  a  column  of  numbers  be  written  ? 
Ans.  So  that  units  may  stand  under  units,  and 
tens  under  tens. 

Write  the  following : — Four  tens,  three  units ; 
nine  tens,  nine  units ;  three  tens,  seven  units ; 
eight  tens,  two  units ;  five  tens,  two  units ;  two 
tens,  five  units ;  one  ten  ;  seven  tens. 

Read  the  numbers  just  written. 

Mention  the  tens  and  units  in  the  following 
numbers,  and  then  read  them : — 80  (eight  tens, 
eighty] ;  75  (seven  tens,  five  units,  seventy-five) ; 
69  ;  93  ;  41 ;  28  ;  7 ;  50  ;  17  ;  32  ;  84 ;  22  ;  61 ; 
14  ;  57  ;  46  ;  70  ;  11 ;  98 ;  23. 

"Which  is  greater,  a  ten  or  a  unit  ? 

How  can  you  turn  three  into  thirty  ? 

Count  from  100  to  75  backwards.  Count 
from  50  to  20  backwards. 

Write  down  in  columns  the  numbers  in  order, 
going  backwards  from  100  to  1. 


12  HUNDREDS. 


LESSON    X. 

How  much  do  10  tens  make  ? 

Ans.  One  hundred — 100. 

Which  figure  shows  the  number  of  hundreds  ? 

Ans.  The  third  figure — 1. 

How,  then,  do  we  write  two  hundred? 

Ans.  By  putting  a  2  in  the  third  place — 200. 

Learn  the  even  hundreds  : — 


One  hundred  100 

Two  hundred  200 

Three  hundred  300 

Four  hundred  400 


Five  hundred  500 

Six  hundred  600 

Seven  hundred  TOO 

Eight  hundred  800 


Nine  hundred  ...     900 

How  many  times  greater  is  1  in  the  third 
place  than  1  in  the  second  place  ? 

Ans.  Ten  times  ;  100  is  ten  times  10. 

What  is  the  effect,  then,  of  removing  a  figure 
one  place  to  the  left? 

Ans.  Its  value  is  increased  ten  times. 

Name  the  places,  going  from  right  to  left. 

Ans.  UNITS,  TENS,  HUNDREDS. 

Count  from  100  to  200.  Thus :—  One  hun- 
dred and  one^  one  hundred  and  two,  &c. 

Write  the  numbers  from  100  to  200.     Thus : 

101  104    107     110     113     116 

102  105     108     111     114     117 

103  106     109     112     115     118,  &c. 


NUMERATION. NOTATION.  13 

LESSON    XI. 

What  is  Numeration  ? 

Answer.  The  art  of  reading  numbers. 

What  is  Notation  ? 

Answer.  The  art  of  writing  numbers. 

I 

EXERCISE    IN    NUMERATION. 

Read  the  following  numbers  : — 


198 

912 

15 

853 

4 

909 

611 

1 

268 

309 

200 

88 

82 

79 

41 

470 

224 

625 

703 

816 

526 

6 

36 

64 

434: 

349 

62 

518 

147 

517 

EXERCISE   IN   NOTATION. 

Write  these  numbers  in  figures  : — 
Eighty-three ;   Fourteen  ;   Two  'hundred  and 
sixty  ;  Nine  hundred  and  forty-eight ;  One  hun- 
dred  and  nine;    Twelve;    Ninety-one;     Seven 
hundred  and  fifty-seven ;  Thirty-four. 

Three   hundred   and   fifteen  ;    Seventy -two  ; 

Six  hundred  and  twenty-four  ;    One  hundred  ; 

|  Four   hundred   and  seven  ;  Eight  hundred  and 

eleven  ;  Eighty-eight ;  Five  hundred  and  forty ; 

Fifty  ;  Seven  hundred  and  twenty  ;  Ninety-nine. 

COUNTING.— Count  from  800  to  900. 


ADDITION. 


LESSON    XII. 


Look  at  the  picture.  You  see  one  chimney  in 
one  part  of  the  roof,  and  one  chimney  in  another 
part ;  how  many  chimneys  do  you  see  in  all  ? 
Count  them.  One  and  one  are — how  many  ?. 

One  sheep  is  feeding  by  itself,  and  two  sheep 
are  feeding  together ;  how  many  sheep  are  there 
in  all  ?  One  and  two  are  — . 

One  boy  and  three  girls  are  walking.  How 
many  in  all  are  walking  ?  One  and  three  are  — . 

One  dog  is  lying  down,  four  dogs  are  running ; 
how  many  dogs  are  there  altogether  ?  One  and 
four  are  — . 


ADDITION.  15 


There  is  one  window  on  one  side  of  the  house, 
and  five  windows  on  another.  How  many  win- 
dows are  there  altogether  ?  One  and  five  are  — . 

There  is  one  girl  jumping  the  rope,  and  six 
girls  not  jumping  it.  Plow  many  girls  are  there 
in  all?  One  and  six  are  — . 

On  the  lawn  we  see  one  boy  and  seven  girls ; 
counting  the  boy  and  girls  together,  how  many 
are  on  the  lawn?  One  and  seven  are  — . 

One  tree  stands  on  one  side  of  the  house,  and 
eight  trees  on  the  other.  How  many  trees  do 
you  count  altogether  ?  One  and  eight  are  — . 

One  chicken  by  itself,  and  nine  chickens  in  a 
group  ;  how  many  chickens  in  all  ?  One  and 
nine  are  — . 

One  hen  and  ten  chickens  ;  counting  hen  and 
chickens  together,  how  many  do  you  find  ?  One 
and  ten  are  — . 

"What  yon  have  just  answered,  will  now  be 
put  in  a  table.  Learn  it  perfectly. 

1  and  1  are  2.     I     1  and     6  are     7. 
1  and  2  are  3.         1  and     7  are     8. 


1  and  3  are  4. 
1  and  4  are  5. 
1  and  5  are  6. 


1  and  8  are  9. 
1  and  9  are  10. 
1  and  10  are  11. 


• 

When  you  put  numbers  together,  to  find  how 
much  they  make,  what  is  the  process  called  2 
A?is.  Addition. 


16 


ADDITION. 


LESSON    XIII. 

TYTiatis  Addition? 

Ans.  Addition  is  the  process  of  uniting  two 
or  more  numbers  in  one. 

"When  you  unite  two  or  more  numbers  in  one, 
what  do  you  find  ?  Ans.  I  find  their  Sum. 


Two  men  are  riding ;  one  is  walking  by  their 
side ;  how  many  men  does  that  make?  Add  2  and  1. 

Jane  has  two  kittens  ;  her  sister  also  has  two. 
How  many  kittens  have  both  ?  Add  2  and  2. 

Jane  had  two  dollars,  and  her  father  gave  her 
three  more.  How  many  had  she  then  ? 


Learn  the  Tables  so  as  to  say  them  forward 
and  backward,  in  order  or  skipping  about. 


2  and 
2  and 


are  3. 
are  4. 


2  and  3  are  5. 
2  and  4  are  6. 
2  and  5  are  7. 


2  and  6  are  8. 
2  and  7  are  9. 
2  and  8  are  10. 
2  and  9  are  11. 
2  and  10  are  12. 


ADDITION.  17 


LESSON    XIV. 


3  and  1  are  4. 

3  and  2  are  5. 

3  and  3  are  6. 

3  and  4  are  7. 

3  and  5  are  8. 


3  and  6  are  9. 
3  and  7  are  10. 
3  and  8  are  11. 
'3  and  9  are  12. 
3  and  10  are  13. 


[Let  the  pupil  in  all  cases  add  each  number  as  a  whole, 
and  not  "by  counting  or  taking  one  unit  at  a  time.  Say  three 
and  three  are  six  ;  not  three,  four,  Jive,  six.] 

1.  A  regiment  marched  three  miles  before 
dinner,  and  five  miles  after  dinner.     How  far 
did  it  march  in  all  ?     Add  3  and  5. 

2.  If  you  have  3  marbles  in  one  pocket,  and 
7  in  another,  how  many  have  you  in  both  ? 

3.  Three  horses  are  in  the  stable,  and  six  are 
in  the  field.     How  many  horses  in  all  ? 

4.  Ruth  bought   three   books;   she  had  ten 
books  before.     How  many  has  she  now  ? 

Now  you  have  some  sums  in  addition  to  do 
on  your  slate.  Copy  the  figures  in  each  column, 
add  them,  and  set  down  the  sum  below  the  line. 

1127859       10 
12331321 


1          10         9         8        74        65        7 
1  1         1         2        10        21         1 

1  1         2         1         12        11        2 


18 


ADDITION. 


LESSON    XV. 

How  many  are  1  and  4?  ->{•     'J'-/Hcvr 

How  many  are  4  and  1  ?  •/Hcww     w 

How  many  are  2  and  4  ?     4  and  2  ? 
How  many  are  3  and  4  ?     4  and  3  ? 
When  you  are  adding  numbers,  does  it  make 
any  difference  which  you  take  first  ? 

Here  are  four  eggs  in 
one  bird's-nest,  four  in 
another;  count  how  many 
there  are  in  both.  Add 
4  and  4. 


Four  kittens  are  running  one  way,  and  five 
the  other ;  how  many  in  all  ?     4  and  5  make  — . 


Four  kittens  and  six  rats  ;  how  many  do  they 


make  together  ? 


How  many  are  4  and  6  ? 


4  and  1  are  5. 
4  and  2  are  6. 
4  and  3  are  7. 
4  and  4  are  8. 
4  and  5  are  9. 

4  and     6  are  10. 
4  and     7  are  11. 
4  and     8  are  12. 
4  and     9  are  13. 
4  and  10  are  14. 

SUMS   IN   ADDITION.  19 

LESSON    XVI. 

1.  Harry  gets  four  good  marks  on  Monday, 
and  seven  more  on  Tuesday ;  how  many  does  he 
get  both  days  ?     How  many  do  4  and  7  make  ? 

2.  I  have  four  fingers  on  each  hand ;  how 
many  have  I  on  both  ?     What  is  the  sum  of  4 
and  4? 

3.  If  four  cars  leave  in  one  train,  and  ten  in 
another,  how  many  leave  in  both  ?     Add  4  and  10. 

4.  Ida  had  one  pencil,  then  she  bought  three, 
and  the  next  day  her  father  gave  her  seven  more ; 
how  many  had  she  then  in  all?     1,  3,  and  7, 
make  how  many  ? 

5.  A  toyman  sold  two  dolls  in  the  morning, 
two  in  the  afternoon,  and  nine  in  the  evening ; 
how  many  did  he  sell  altogether  ?     2  and  2  added 
to  9  make  how  many  ? 

6.  If  I  give  four  dollars  for  a  vest,  and  eight 
dollars  for  a  coat,  how  much  do  both  cost  me  ? 

Do  the  following  sums  on  your  slate.  Be 
sure  to  set  units  under  units,  tens  under  tens. 

Add  twenty-three  and  thirty-four.  Add  one 
hundred,  twelve,  and  three  hundred  and  forty- 
three.  Add  forty -four  to  four  hundred  and  one. 
Add  four  and  eleven.  Add  seventy-four  and 
two  hundred  and  two.  Add  ninety-four  and 
three  hundred. 


20 


ADDITION. 


LESSON   XVII. 


How  many  are  one  and  five  ?  •>(•  -JHH 
How  many  are  five  and  one  2   -JHHHH 
How  many  are  2  and  5  ?     5  and  2  ? 
How  many  are  3  and  5  ?     5  and  3  ? 


Five  lilies  and  four  roses ;  how  many  of  both  ? 


Five  boys  are  sailing  in  one  boat,  and  five  in 
another.     Count  how  many  there  are  in  both. 


Five  tops  are  lying  on  the  floor,  and  six  are 
spinning ;  how  many  do  you  see  in  all  ? 

How  many  are  5  and  7?       11111    1 1  I  1  1  I  I 
How  many  are  5  and  8?       Mill    I  I  Ml  II  I 
How  many  are  5  and  9?       Mill    I  Mill  III 
How  many  are  5  and  10?     Mill    M  I  I  II  11  I  I 
"Which  is  the  greater,  five,  or  ten  ? 


5  and  1  are  6. 

5  and  2  are  7. 

5  and  3  are  8. 

5  and  4  are  9. 

5  and  5  are  10. 


5  and     6  are  11. 

5  and     7  are  12. 

5  and     8  are  13. 

5  and     9  are  14. 

5  and  10  are  15. 


SUMS   IN   ADDITION.  21 


LESSON    XVIII. 

1.  Five  years  ago  Mary  was  nine  years  old ; 
how  old  is  she  now  ?     How  much  are  5  and  9  ? 

2.  We  have  five  toes  on  each  foot ;  how  many 
toes  have  we  in  all  ?     What  is  the  sum  of  5  and  5  ? 

3.  Horace  has  five  marbles  in  one  bag,  and 
ten  in  another  ;  how  many  has  he  in  both?    Add 
5  and  10. 

4.  Five  pigs  are  in  the  orchard,  and  seven  in 
the  sty.     How  many  pigs  are  there  altogether  ? 

5.  Louise   has  three  cents,  Mary  two,   and 
George  eight ;  how  many  cents  have  all  three  ? 

6.  Susan  has  four  books  ;  if  her  brother  gives 
her  one  more,  and  her  sister  two,  how  many  books 
will  she  have  ?     Add  4,  1,  and  2. 

7.  Richard  caught  five  fish,  and  Ben  six  ;  how 
many  did  both  catch  ?     How  many  are  5  and  6  ? 

8.  The  first  story  of  a  house  contains   two 
rooms,  the  second  three,  and  the  third  three  ;  how 
many  rooms  does  the  whole  house  contain? 

Here  are  some  sums  for  your  slate.     Read 
each  of  the  numbers  added,  and  also  the  answers. 

(10)  (11)  (12)  (13)  (14)  (15) 

4  403  927  8  5  765 
14  515  20  610  372  121 
51  30  32  41  112  102 


22 


ADDITION. 


ESSON    XIX 

How  many  are  one  and  six?  ->(-  ->H 
How  many  are  six  and  one  ?  ->HHc"/ 
How  many  are  2  and  (3  ?  6  and  2  ? 
How  many  are  3  and  6  ?  6  and  3  ? 
How  many  are  4  and  6  ?  6  and  4  ? 
How  many  are  5  and  6  ?  6  and  5  ? 


Here  we  have  six  flies  and  six  spiders, 
and  spiders,  how  many  are  there? 


Flies 


Six  squirrels  are  eating,  seven  are  running ; 
count  how  many  there  are  in  all. 


If  you  put  six  forks  and  eight  forks  together, 
how  many  will  that  make  ? 

How  many  are  6  and  9?       1  1  I  I  1 1    I  I  I  I  I  1  I  1  ! 
How  many  are6  andlO?    I  1  I  I  I  I    I  I  I  1  I  I  I  1  1  I 


6  and  1  are  7. 
6  and  2  are  8. 
6  and  3  are  9. 
6  and  4  are  10. 
6  and  5  are  11. 


6  and     6  are  12. 

6  and     7  are  13. 

6  and     8  are  14. 

6  and     9  are  15. 

6  and  10  are  16. 


SUMS   IN   ADDITION.  23 

LESSON    XX. 

1.  Troy  is  six  miles  above  Albany,  and  Lan- 
singburg  is  three  miles  farther  ;  how  far  is  Lan- 
singburg  from  Albany  ?   6  and  3  make  how  many  ? 

2.  If  I  have  6  dollars  in  my  pocket,  and  9  in  my 
purse,  how  much  have  I  in  all  ?     Add  6  and  9. 

3.  Three  dogs,  and  three  dogs,  and  three  dogs, 
make  how  many  ?     How  many  are  3,  3,  and  3  ? 

4.  Two  ships,  four  schooners,  and  ten  brigs, 
are  in  port  ;  how  many  vessels  does  that  make  in 
all  ?     What  is  the  sum  of  2,  4,  and  10  ? 

5.  A  baker  sold  six  loaves  of  wheat  bread,  and 
two  of  rye  ;  how  many  loaves  did  he  sell  in  all  ? 

6.  Mary  gave  a  poor  man  six  cents,  and  Kate 
gave  him  five;  how  much  did  he  receive  from 
l3oth  ?     How  much  are  6  and  5  ? 

7.  If  six  horses  are  in  the  stable,  and  I  put  in 
eight  more,  how  many  will  be  there  then  ? 

8.  Six  goats  and  .one  goat  make  how  many  ? 

9.  Six  shoes  in  one  drawer,  and  six  in  another, 
make  how  many  in  all  ? 

Do  these  sums  in  addition  on  your  slate  :  — 

(10)  (11)  (12)  (13)  (14)  (15) 

80  92  43  66  730  80 
31  25  653  42  10  605 
26  41  203  11  256  113 


137 


24 


ADDITION. 


LESSON    XXI. 


How  many  are  1  and  7  ? 
How  many  are  7  and  1  ? 
How  many  are  2  and  7  ? 
How  many  are  3  and  7? 
How  many  are  4  and  7  ? 
How  many  are  5  and  7  ? 
How  many  are  6  and  7  ? 


7  and  2  ? 

7  and  3? 

7  and  4? 

7  and  5  ? 

7  and  6? 

Mary  has  a  bunch  of  seven 
cherries,  and  buys  seven  more ; 
how  many  has  she  then  ?  Count 
and  see. 


Seven  boys  and  eight  girls  make  how  many 
children  in  all  ?     How  many  are  7  and  8  ? 

Seven  wine  glasses  in  one 
row  and  nine  in  another 
make   how  many  in  all? 
How  many  are  7  and  9  ? 
How  many  are  7  and  10?     1MI1M    II II  111  II I 


7  and  1  are  8. 
7  and  2  are  9. 
7  and  3  are  10. 
7  and  4  are  11. 
7  and  5  are  12. 


and 
and 
and 
and 


6  are  13. 

7  are  14. 

8  are  15. 

9  are  16. 


7  and  10  are  17. 


SUMS   IN   ADDITION.  25 


LESSON    XXII. 

1.  To  get  home,  I  shall  have  to  go  seven  miles 
by  steamboat,  and  five  by  stage;  how  far  will  I 
have  to  travel  ?     What  is  the  sum  of  7  and  5  ? 

2.  A  farmer  had  seven  rooms  in  his  house,  and 
built  a  wing  with  three  rooms  more ;  how  many 
rooms  had  he  then  ?     How  many  are  7  and  3  ? 

3.  A  gardener  set  out  three  lilacs,  four  roses, 
and  ten  verbenas ;  how  many  plants  did  he  set 
out  in  all?    Add  3,  4,  and  10. 

4.  Mary  dressed  five  dolls  for  the  fair,  Augusta 
two,  and  Helen  seven ;  how  many  did  all  three 
dress  ?    How  many  are  5,  2,  and  7  ? 

5.  If  my  black  hen  has  seven  chickens,  and 
my  white  hen  nine,  how  many  have  both  ? 

6.  How  far  will  a  horse  go  in  2  hours,  if  he 
travels  Y  miles  the  first  hour,  and  6  the  second  ? 

7.  How  many  are  6  and  4  ?     5  and  9  ?    4  and 
7?     7  and  4?     7  and  2?     3  and  10?     2  and  8? 
1,  6,  and  1  ?     4,  3,  and  8  ?     6,  1,  and  6  ?     1  and 
7  ?     6  and  3  ? 

Here  are  more  sums  for  your  slate.  Make 
your  figures  neatly.  Eead  each  number,  and  tell 
whether  the  upper  or  lower  one  is  the  greater. 

(8)  (9)  (10)  (11)  (12)  (13) 

163    329    48    856    775    507 
425    670    731    132    11    182 


ADDITION. 


LESSON    XXIII. 


How  many  are  1  and  8  ?  ->(-  wwwww 
How  many  are  8  and  1  ?  -X—  >HHHHH 
How  many  are  2  and  8  ?  8  and  2  ? 
How  many  are  3  and  8  ? 
How  many  are  4  and  8  ? 
How  many  are  5  and  8  ? 
How  many  are  6  and  8  ? 
How  many  are  7  and  8  ? 


*8  and  3  ? 
8  and  4  ? 
8  and  5  ? 
8  and  6  ? 
8  and  7  ? 


Eight  doves  in  one  group,  and  eight  in  another, 
make  how  many  in  all  ?  How  many  are  8  and  8  ? 
Eight  rounds  in  one  ladder,  and 
nine  rounds  in  another,  make  how 
many  rounds  in  all  ?  What  is  the 
sum  of  8  and  9  ? 
Eight  spokes  are  in  one 
wheel,  and  ten  in  another ;  how 
many  are  in  both  ?  8  and  10 
are  — . 


8 

and 

1 

are 

9. 

8 

and 

'  6 

are 

14. 

8 

and 

2 

are 

10. 

8 

and 

7 

are 

15. 

8 

and 

3 

are 

11. 

8 

and 

8 

are 

16. 

8 

and 

4 

are 

12.          8 

and 

9 

are 

17. 

8 

and 

5 

are 

13.     !     8 

and 

10 

are 

18. 

SUMS   IN   ADDITION.  27 


LESSON    XXIV. 

1.  A  lady  bought  eight  cents'  worth  of  needles, 
and  six  cents'  worth  of  thread  ;  how  much  did  she 
lay  out  ?    How  many  are  8  and  6  ? 

2.  Eight  birds  are  sitting  on  a  bush ;  if  ten 
more  alight  b$  their  side,  how  many  will  there 
be  ?     What  is  the  sum  of  8  and  10  ? 

3.  If  I  spend  six  dollars  for  clothes,  two  dol- 
lars for  books,  and  three  dollars  for  groceries,  how 
much  do  I  spend  in  all  ?     6,  2,  and  3,  are  — . 

4.  Sarah  has  three  rabbits,  Ruth  five,  and 
Herman  seven.     If  Sarah  and  Ruth  give  theirs 
to  Herman,  how  many  will  he  have  ?     Add  33 
5,  and  7. 

5.  If  a  dairy-maid   makes  eight  pounds  of 
butter  one  day,  and  four  the  next,  how  many 
does  she  make  in  all  ?     How  many  are  8  and  4  ? 

6.  How  many  boys  will  two  benches  hold, 
if  one  holds  eight   and  the   other  nine  ?     Add 
8  and  9. 

7.  Add  on  your  slate  seventeen  and  eighty. 

8.  Add  twenty  to  two  hundred  and  twelve. 

Read  these  numbers ;  add  them. 

(9)  (10)  (11)  (12)  (13)  (14)  (15) 

63         57        91        40        21        35        72 

82         81         88         88         85         84        85 

"145  157 


28 


ADDITION. 


How 
How 
How 
How 
How 
How 
How 
How 
How 


LESSON    XXV. 

many  are  one  and  nine  ?  f  ttttttttt 
many  are  nine  and  one  ?  ttttttttt  t 
many  are  2  and  9  ?  9  and  2  ? 

9  and  3  ? 

9  and  4  ? 

9  and  5  ? 

9  and  6  ? 


many  are  3  and  9  ? 
many  are  4  and  9  ? 
many  are  5  and  9  ? 
many  are  6  and  9  ? 
many  are  7  and  9  ? 
many  are  8  and  9  ? 


9  and  7  ? 

9  and  8  ? 


stars  in  all  ? 


^  ^  Nine    stars    in    one 

^k^kf^i.    group,  and  nine  in  an- 
other, make  how  many 
Count  and  see. 


If  there  are  nine  cannon- 
balls  in  one  pile,  and  ten  in 
another,  how  many  balls  are 
there  in  both  ?  What  is  the  sum  of  9  and  10  ? 

A  jeweller  has  nine  watches  in  his  safe,  and 
five  on  his  counter  ;  how  many  has  he  in  all  ? 


9  and  1  are  10. 
9  and  2  are  11. 
9  and  3  are  12. 
9  and  4  are  13. 
9  and  5  are  14. 


9  and     6  are  15. 

9  and     7  are  16. 

9  and     8  are  17. 

9  and     9  are  18. 

9  and  10  are  19. 


SUMS   IN   ADDITION.  29 


LESSON    XXVI. 

1.  If  Harry  has  nine  dollars  in  the  bank,  and 
four  in  his  pocket,  how  much  has  he  in  all  ? 

2.  A  milkman  sold  one  customer  three  quarts 
of  milk,  another  six  quarts,  and  a  third  seven ; 
how  many  quarts  did  he  sell  all  three?     What  is 
the  sum  of  3,  6,  and  7  ? 

3.  Blanche  has  two  canary  birds,  Rose  seven, 
and  Alice  three ;  if  Eose  and  Alice  give  theirs 
to  Blanche,  how  many  will  she  then  have  ? 

4.  If  one  field  yields  nine  bushels  of  potatoes, 
and  aixother  ten,  how  much  do  both  yield  ? 

5.  If  Frank  gets  nine  good  marks  in  the  morn- 
ing, and  five  in  the  afternoon,  how  many  does  he 
get  during  the  day  ?     How  many  are  9  and  5  ? 

6.  Nine  currants  on  one  string,  and  nine  on 
another,  make  how  many  currants  in  all  ?     9  and 
9  are  how  many  ? 

7.  There  are  nine  eggs  in  one  hen's  nest,  and 
six  in  another  ;  if  we  put  the  eggs  together,  how 
many  will  there  be  ?   What  is  the  sum  of  9  and  6  ? 

8.  What  is  the  sum  of  1,  8,  and  2  ? 

Read  the  following  numbers.     Add  them. 

(9)  (10)  (11)  (12)  (13)  (14) 

510    601    17    82    140    91 

67    95    700    33    806    45 

412    203    41    62    42    52 


30  ADDITION. 


LESSON    XXVII. 

How  many  are  one  and  ten  ? 

How  many  are  ten  and  one  ? 

How  many  are  2  and  10  ?     10  and  2  ? 

How  many  are  3  and  10  ?     10  and  3  ? 

How  many  are  4  and  10  ?     10  and  4  ? 

How  many  are  5  and  10  ?     10  and  5  ? 

How  many  are  6  and  10  ?     10  and  6  ? 

How  many  are  7  and  10  ?     10  and  7  ? 

How  many  are  8  and  10  ?     10  and  8  ? 

How  many  are  9  and  10  ?     10  and  9  ? 

How  many  are  two  tens  ?     Ans.  Twenty.    10 

How  many  are  ten  and  ten  ? 

You  have  eight  fingers  and  two  thumbs  ;  I 
have  the  same.  How  .many  fingers  and  thumbs 
have  we  together?  What  is  the  sum  of  8,  2, 
and  10  ? 

A  dime  is  worth  ten  cents ;  a  half-dime  is 
worth  five  cents.  How  many  cents  are  both 
together  worth  ?  How  many  are  10  and  5  ? 

What  is  the  sum  of  7,  3, 'and  8  ? 

What  is  the  sum  of  6,  4,  and  3  ?  • 


10  and  1  are  11. 

10  and  2  are  12. 

10  and  3  are  13. 

10  and  4  are  14. 

10  and  5  are  15. 


10  and  6  are  16 
10  and  7  are  17. 
10  and  8  are  18. 
10  and  9  are  19 
10  and  10  are  20. 


THE   EVEN   THOUSANDS.  31 


LESSON   XXVIII. 

What  is  the  greatest  number  that  can  be 
expressed  with  one  figure  ? 

Ans.  Nine  (9). 

If  you  add  1  to  9,  what  do  you  get  ? 

Ans.  Ten  (10). 

What  is  the  greatest  number  that  can  be 
expressed  with  two  figures  ? 

Ans.  Ninety-nine  (99). 

If  you  add  1  to  99,  what  do  you  get  ? 

Ans.  One  hundred  (100). 

What  is  the  greatest  number  that  can  be 
expressed  with  three  figures  ? 

Ans.  Nine  hundred  and  ninety-nine  (999). 

If  you  add  1  to  999,  what  do  you  get  ? 

Ans.  One  thousand  (1000). 

How  many  figures  are  used  in  writing  1000? 

What  figure  shows  the  number  of  thousands  ? 

Ans.  The  fourth  figure — 1. 

How,  then,  do  we  write  two  thousand? 

Ans.  By  putting  a  2  in  the  fourth  place 

Learn  the  even  thousands  : — 


One  thousand  1000 

Two  thousand  2000 

Three  thousand  3000 

Four  thousand  4000 


Five  thousand  5000 

Six  thousand  6000 

Seven  thousand  7000 

Eight  thousand  8000 


Nine  thousand  .     .     .  9000 


32  EXERCISE   IN   NOTATION. 

LESSON    XXIX. 

Learn  the  even  hundreds  between  1000  and 
2000  :— 

1100,  one  thousand  one  hundred,  or  eleven  hundred. 
1200,  one  thousand  two  hundred,  or  twelve  hundred. 
1300,  one  thousand  three  hundred,  or  thirteen  hundred. 
1400,  one  thousand  four  hundred,  or  fourteen  hundred. 
1500,  one  thousand  five  hundred,  or  fifteen  hundred. 
1600,  one  thousand  six  hundred,  or  sixteen  hundred. 
1700,  one  thousand  seven  hundred,  or  seventeen  hundred. 
1800,  one  thousand  eight  hundred,  or  eighteen  hundred. 
1900,  one  thousand  nine  hundred,  or  nineteen  hundred. 
2000,  two  thousand. 

Write  on  your  slate  the  numbers  between  1000 
and  1100,  and  then  read  them.     Thus  : 

1001,  one  thousand  and  one. 

1002,  one  thousand  and  two,  &c 
Write  one  thousand  and  ten.  1010. 
Write  two  thousand  and  ten.                     2010. 
Write  1  thousand  2  hundred  and  ten.      1210. 
Write  8  thousand  2  hundred  and  ten.      8210. 
Write  one  thousand  four  hundred.           1400. 
Write  six  thousand  four  hundred.             6400. 
Name  the  places,  going  from  right  to  left. 
Ans.  UNITS,  TENS,  HUNDREDS,  THOUSANDS. 
Read  and  then  add  the  following  numbers : — 

1024        1031         1059         1400        1099 
2024         3031         4000         5000         1600 


NOTATION,    NUMERATION.  33 

LESSON    XXX. 

What  place  denotes  thousands  ? 
Ans.  The  fourth  place. 

How  do  you  write  five  thousands,  nine  hun- 
dreds, seven  tens,  one  unit  ? 

Ans.  5  in  the  fourth  place  denotes  five  thou- 
sands ;  9  in  the  third  place,  nine  hundreds ;  7 
in  the  second  place,  seven  tens ;  1  in  the  first 
place,  one  unit.  Thus  we  get  5971. 

Read  this  number. 

Ans.  Five  thousand  nine  hundred  and  seventy- 
one. 

Write  the  following,  placing  units  under  units, 
tens  under  tens,  &c.  :  Four  thousands,  8  hun- 
dreds, 6  tens,  2  units ;  five  thousands,  3  hun- 
dreds, 1  ten,  1  unit ;  nine  thousands,  2  hundreds, 
8  tens,  7  units  ;  seven  thousands,  4  hundreds. 

Eead  the  numbers  just  written. 

Mention  the  thousands,  hundreds,  tens,  and 
units,  in  the  following  numbers : — 4629  ;  9780 ; 
5111 ;  1236  ;  7405  ;  2293  ;  529  ;  18. 

When  a  naught  stands  in  the  third  or  second 
place,  must  you  say  no  hundreds,  no  tens  f 

Ans.  No ;  it  is  passed  over  in  reading.  Thus, 
9007  is  read  nine  thousand  and  seven. 

Kead  7012  ;  6099  ;  3003  ;  8064;  1011;  5002. 


34:  NOTATION,    NUMERATION,    COUNTING. 

LESSON    XXXI. 

Write  the  following  numbers  with  figures  : — 
One  thousand  six  hundred  and  fifty-three. 
Five  thousand  nine  hundred  and  eighteen. 
Seven  thousand  eight  hundred  and  ninety. 
Three  thousand  five  hundred  and  seven. 
Eight  thousand  and  forty-nine. 
Eead  the  following  numbers  : — 4321 ;  2906  ; 
6870 ;  5012  ;  1864 ;  9990 ;  1007 ;  8700 ;  3401. 

When  we  count,  one,  two,  three,  four,  &c.5 
how  do  we  get  each  number  ? 

Ans.  By  adding  1  to  the  number  going  before. 
Now  in  stead  of  adding  1,  add  2  each  time : 

1          7        13        19        25  31  37 

3          9        15         21        27  33  39 

5         11        17        23        29  35  41 

and  so  on  to  99. 

In  adding  units,  if  the  sum  is  9,  what  do  we  do  ? 

Ans.  We  set  down  the  9  in  the  units'  place. 

If  the  sum  is  10,  what  do  we  do  ? 

Ans.  10  consists  of  0  units,  1  ten.  6 
Hence  we  set  0  in  the  first  or  units'  place,  _^ 
and  1  in  the  second  or  tens'  place. 

Whenever  the  sum  consists  of  two  figures,  how 
must  we  place  them  ? 

Ans.  Set  the  right-hand  figure  in  the  units' 
place,  the  left-hand  figure  in  the  tens'  place. 


CARRYING   IN    ADDITION.  35 

LESSON    XXXII. 

Add  the  following  numbers  : — 

(1)  (2)  (3)      '     (4)  (5)  (6)  (7) 

4:  5  8  7  9  4  9 
3  4  1  31  11 
2342211 

1        2        3        4        5        6        7 

26  Now  look  at  this  sum.  Begin  to  add  at 
17  the  right.  7.  and  6  are  13 — three  units  and 
43  1  ten.  "We  set  down  3  in  the  units'  place, 
and  as  there  are  other  tens  we  add  our  1  ten 
in  with  them,  making  4,  which  we  set  down  in 
the  tens'  place.  Answer,  43. 

What  is  this  process  called  ? 

Ans.  Carrying.  In  the  given  sum,  we  carried  1. 

When  must  we  carry  in  addition  ? 

Ans.  Whenever,  in  adding  a  column  of  fig- 
ures, we  find  their  sum  is  over  9. 

What  is  the  rule  for  carrying  ? 

Ans.  Set  down  the  right-hand  figure,  and 
carry  the  left-hand  figure  to  the  next  column. 

If  the  sum  of  a  column  is  34,  which  figure 
must  be  set  down,  and  which  carried  ? 

Ans.  Set  down  4,  and  carry  3. 

What  do  you  set  down,   and  what  do 
carry,  if  the  figures  added  make   96?     If  they 
make  71;  80  ;  52  ;  11 ;  48  ;  84  ;  17/ 


36  ADDING   COLUMNS   ALOUD. 


LESSON    XXXIII. 

Look  at  this  sum.     Learn  to  add  each  column 
aloud,  in  the  following  manner  : — 

1959          IST  COLUMN. — Two,  five,  six,  eight,  seven- 
<jown  7  and  carry  1. 

7  * 

2o  COLUMN. — One,  five,  seven,  ten,  fif- 

1342     ^een — se^  down  5>  and  Can7  1- 
rr^z          3o    COLUMN. — One,   four,    six,  nine, 
eighteen — set  down  8,  and  carry  1. 

4'ra  COLUMN. — One,   two,  four,  seven,   eight, 
nine — set  it  down. 

Answer,  nine  thousand  eight  hundred   and 
fifty-seven. 

Add  the  following  in  the  same  way,  not  on 
the  slate,  but  aloud. 

(1)  (2)  (3)  (4)  (5) 

112  1270  1492  1666  374 

22  321  2101  1022  311 

332  2011  2121  232  1002 

232  3322  1060  2432  2123 

211  1346  2714  4212  5463 


909    8270    9488    9564    9273 

Commencing  with  2,  give  the  numbers  formed 
by  adding  2  each  time,  up  to  100.  Thus  : — 

2    6    10    14    18    22    26 

4    8    12    16    20    24    28,  &c. 


ADDING   THREE.  37 


LESSON   XXXIV. 

Do  the  following  sums  on  your  slate.  Set 
down  the  figure  carried,  beneath  each  column, 
in  the  space  left. 

(1)  (2)  (3)  (4) 

1228  3222  1252  2122 

1654  222  2202  1422 

2343  2222  1942  1465 

3421  3965  2749  4358 

Carried 

How  much  are  3  and  3  ?     3  and  13  ? 

How  much  are  3  and  4  ?     3  and  34  ? 

How  much  are  3  and  5  ?     3  and  45  ? 

How  much  are  3  and  6  ?     3  and  66  ? 

How  much  are  3  and  7?     3  and  87? 

Which  is  greater,  900  or  700  ?     900  or  1000  ? 

Which  is  greater,  1  hundred  or  1  thousand  ? 

Commencing  with  3,  give  the  numbers  formed 
by  adding  3  each  time  : — 

3  18  33  48  63  78  93 

6  21  36  51  66  81  96 

9  24  39  54  69  84  99 

12  27  42  57  72  87  102 

15  30  45  60  75  90  105 

If  I  have  27  roses,  and  buy  3  more,  how  many 
will  I  then  have  ?  If  some  one  gives  me  three 
more,  and  I  raise  3  from  slips,  how  many  will  I 
then  have  in  all  ? 


38 


ADDING   FOUR. 


LESSON     XXXV. 

How  many  are  4  and  4  ?  4  and  14  ?  4  and 
4and34?  4and44?  4and54?  4and64? 
How  many  are  4  and  5  ?  4  and  75  ?  4  and  85  ? 
How  many  are  4  and  6  ?  4  and  86  ?  4  and  96  ? 
How  many  are  4  and  7  ?  4  and  47?  4  and  57? 


Robert  has  8  fish  in  his  basket  and  4  on  the 
grass ;  how  many  has  he  in  all  ?  How  many 
are  8  and  4  ?  18  and  4  ?  28  and  4  ?  48  and  4,? 

How  many  are  4  and  9  ?   4  and  89  ?   34  and  9  ? 

Commencing  with  4,  give  the  numbers  formed 
Thus  :— 


by  adding  4  each  time. 


4 
8 

12 
16 


20 
24 

28 
32 


36 
40 
44 

48 


52 
56 
60 
64 


68 
72 
76 
80 


84 
88 
92 
96 


ADDING   FIVE.  39 


LESSON    XXXVI. 

How  many  are  5  and  5  ?  5  and  15  ?  5  and 
25  ?  5  and  45  ? 

How  many  are  5  and  6  ?  5  and  26  ?  5  and 

36  ?  5  and  46  ?  5  and  56  ?  55  and  6  ?  5  and 
66  ?  65  and  6  ? 

How  many  are  5  and  7  ?  5  and  77  ? 

How  many  are  5  and  8  ?  5  and  88  ? 

How  many  are  5  and  9  ?  5  and  29  ?  25  and 

9  ?  5  and  49  ?  45  and  9  ?  5  and  59  ?  5  and  69  ? 

Commencing  with  5,  give  the  numbers  formed 
by  adding  5  each  time.  Thus  : — 

5  20  35  50  65  80  95 
10  25  40  55  70  85  100 
15  30  45  60  75  90  105 

What  do  these  numbers  end  in  ? 


1.  John  had  twenty  cents ;  his  mother  gave 
him  five,  and  his  father  five  more.     How  many 
had  he  then?     How  many  are  20,  5,  and  5 ? 

2.  Forty-eight  apples  in  one  basket,  and  five 
in  another,  make  how  many  apples  in  all  ? 

3.  A  traveller  rode  thirty-nine  miles  one  day, 
and  five  miles  the  next.     How  far  did  he  ride 
both  days  ?     Add  39  and  5. 

4.  I  have  just  found  five  pins,  said  Eli,  and  I 
had  seventeen  before.     How  many  have  I  now  ? 


40  ADDITION. 


LESSON    XXXVII. 

How  many  are  6  and  6  ?  6  and  16  ?  46  and  6  ? 
How  many  are  6  and  7  ?  6  and  27  ?  27  and  6  ? 

How  many  are  6  and  8  ?  6  and  88  ?  38  and 
6  ?  58  and  6  ?  How  many  are  6  and  9  ?  6  and 
99  ?  29  and  6  ? 

How  many  are  7  and  7  ?  7  and  47  ?  87  and 
7?  How  many  are  7  and  8?  7  and  58?  28 
and  7  ?  How  many  are  7  and  9  ?  69  and  7  ? 

How  many  are  8  and  8  ?  8  and  78  ?  18  and 
8?  How  many  are  8  and  9  ?  8  and  99?  68 
and  9?  69  and  8  ? 

How  many  are  9  and  9  ?   9  and  59  ?  79  and  9  ? 

How  many  are  10  and  2  ?  40  and  2  ?  6  and 
10  ?  6  and  60  ?  10  and  8  ?  90  and  8  ?  10  and 
9  ?  9  and  100  ?  30  and  3  ? 


1.  There  are  twenty-nine  girls  in  one  class, 
and  eight  in  another  ;  how  many  in  both  ? 

2.  How  many  apple-trees  have  I  on  my  farm, 
if  there  are  27  in  one  field  and  6  in  another  ? 

3.  A  half  dollar  is  worth  fifty  cents,  and  a 
dime  ten  cents.     How  much  are  both  worth  ? 

4.  Nine  pigeons  join  a  flock  of  thirty-eight. 
How  many  does  the  flock  then  contain  ? 

5.  Sixteen  roses  in  one  bouquet,  and  eight  in 
another,  make  how  many  in  both  ? 


SUMS   IN   ADDITION.  41 


LESSON    XXXVIII. 

Read  the  following  numbers  in  turn.     Add 
aloud  (not  on  the  slate),  as  shown  on  page  36. 

(1)  (2)  (3)  (4) 

546  145  834  689 

3063  2083  1045  1989 

789  1978  626  3754 

4261  939  3997  1965 

825  1987  1698  876 


9484  7132  8200  9273 

Now  you  have  some  sums  for  the  slate.     Be 
sure  to  set  units  under  units,  tens  under  tens,  &c. 

1.  Add  ninety-nine;   eighty-seven;  fifty-six; 
twenty-four  ;  and  one  hundred  and  eight. 

2.  Add  four  hundred   and  fifty ;  nineteen  ; 
eight  thousand  six  hundred  and  nine ;  seven  hun- 
dred and  twenty-three  ;  and  eighty -four. 

3.  Add    two    thousand   four   hundred   and 
twenty-one ;    nine    hundred   and    eighty-seven ; 
eighteen  hundred  and  ninety-nine ;  three   thou- 
sand and  sixteen ;  nine  hundred  and  ninety-nine. 

4.  Add  three  thousand  and  eight ;  nine  hun- 
dred and  ninety ;  seventeen  hundred  and  fifty-six  ; 
five  hundred  and  ninety-seven;    two   thousand 
eight  hundred  and  eighty-eight. 

What  is   Numeration?     What   is  Notation? 
What  is  Addition? 


SUBTRACTION. 


LESSON    XXXIX. 


the 
away ; 


Two    pigeons    were    on 
ground.     One  has  flown 
how  many  are  left  ? 

Two  cows  were  standing 
near  a  pond.  One  of  them  has 
gone  into  the  water ;  how 
many  are  left  on  the  bank  ? 

Take  1  from  2,  and  what  is  left  \ 

What  is  this  process  called  ? 

Ans.  Subtraction. 

What  is  Subtraction  ? 

Ans.  Subtraction  is  the  process  of  taking  one 
number  from  another. 

When  we  count  one,  two,  three,  four,  &c., 
how  do  we  get  each  number  ? 

Ans.  By  adding  1  to  the  number  going  before. 

When  we  count  backward,  ten,  nine,  eight, 
&c.,  how  do  we  get  each  number  ? 

Ans.  By  subtracting  1  each  time  from  the 
number  going  before. 

Count  backward  from  100  to  1. 


1  from  1  leaves  0. 
1  from  2  leaves  1. 
1  from  3  leaves  2. 
1  from  4  leaves  3. 
1  from  5  leaves  4. 

1  from     6  leaves  5. 
1  from     7  leaves  6. 
1  from     8  leaves  7. 
1  from     9  leaves  8. 
1  from  10  leaves  9. 

SUBTRACTION. 


LESSON    XL. 

What  is  Subtraction  ? 

When  we  take  one  number  from   another, 
what  is  the  result  called  ? 
Ans.  The  Remainder. 


Three  boys  were  riding.  Two  got  out  to 
gather  berries ;  how  many  were  left  in  the  wagon  ? 

Four  dogs  ran  barking  after  the  wagon.  Two 
have  turned  back  ;  how  many  are  left  there  ? 

Five  cows  were  standing  in  afield.  Two  have 
lain  down ;  how  many  remain  standing  ? 


2  from  2  leaves  0. 
2  from  3  leaves  1. 
2  from  4  leaves  2. 
2  from  5  leaves  3. 
2  from  6  leaves  4. 


2  from     7  leaves  5. 

2  from     8  leaves  6. 

2  from     9  leaves  7. 

2  from  10  leaves  8. 

2  from  11  leaves  9. 


44  SUMS   IN   SUBTRACTION. 

LESSON    XLI. 

Which  of  two  numbers  must  we  take  from 
the  other,  to  find  their  difference  ? 

Ans.  We  must  take  the  less  from  the  greater. 


1.  Susan  has  six  apples,  and  gives  away  two  ; 
how  many  has  she  left  ? 

2.  If  John  has  ten  marbles,  and  loses  one, 
how  many  has  he  then? 

3.  A  man  having  five  sheep,  sold  one ;  how 
many  remained  unsold  ? 

4.  Mary  gives  a  beggar  two  cakes.     She  had 
nine  before ;  how  many  has  she  left  ? 

5.  If  there  are  two  boys  in  a  class  of  seven 
children,  how  many  girls  are  in  the  class  ? 

6.  2  from  4  leaves  how  many  ?     2  from  24  ? 
2  from  54  ?     2  from  74  ? 

7.  Two  from  6,  how  many  ?     2  from  96  ? 

8.  Two  from  8,  how  many  ?     2  from  48  ?     2 
from  78  ?     2  from  38  ? 

Commencing  with  50,  give  the  numbers  ob- 
tained by  subtracting  2  each  time.  Thus:  50, 
48,  46,  44,  42,  40,  38,  36,  34,  32,  30,  &c. 


SUMS    FOE    THE    SLATE. 

From 
Take 

Remainder 

(1) 

98 
12 

(2) 

891 
120 

(3) 

437 
121 

(4) 

1652 
212 

(5) 

7234 
2112 

SUBTRACTION. 


LESSON    XLII. 

What  is  Subtraction?     What  is  the  answer 
called  in  a  sum  in  Subtraction  ? 


There  are  4  panes  of  glass  in  this  barn  win- 
dow. If  3  are  broken,  how  many  are  unbroken  ? 

There  were  five  sheep  in  the  barn-yard,  but 
three  have  gone  into  the  field.  How  many 
remain  ?  Count  them  in  the  picture. 

Nine  chickens  were  on  the  ground ;  3  have 
gone  to  roost.  How  many  are  left  on  the  ground  ? 


3  from  3  leaves  0. 
3  from  4  leaves  1. 
3  from  5  leaves  2. 
3  from  6  leaves  3. 
3  from  7  leaves  4. 


3  from  8  leaves  5. 
3  from  9  leaves  6. 
3  from  10  leaves  7. 
3  from  11  leaves  8. 
3  from  12  leaves  9. 


SUBTRACTION. 


LESSON   XLIII. 

Take  four  oxen  from  four  oxen, 
and  how  many  are  left  ?     Cover 
four  over,  and  count  the  rest.     4 
from  4  leaves  how  many  ? 

Take  four  eggs  from  a  nest  con- 
taining five,  and  how  many  remain  ? 
Cover  4,  and  count  the  rest. 

Here  is  a  knife  with  six  blades. 
If  4  of  them  are  closed,  how  many 
are  open  ?  4  from  6  leaves  how  many  ? 

Here  are  seven  flowers  on  one 
stem,  but  four  are  broken ;  how  many 
are  unbroken  ? 

wwww     •JHHHr     From  eight  stars  take 
four  stars  ;  how  many  are  left  ? 

A  lady  having  nine 
wine  glasses,  broke  four 
of  them ;  how  many  had  she  left  ? 

Four  from  ten  leaves  how  many  ? 


4  from  4  leaves  0. 
4  from  5  leaves  1. 
4  from  6  leaves  2. 
4  from  7  leaves  3. 
4  from  8  leaves  4. 


4  from     9  leaves  5. 

4  from  10  leaves  6. 

4  from  11  leaves  7. 

4  from  12  leaves  8. 

4  from  13  leaves  9. 


SUMS   IN    SUBTRACTION.  47 


LESSON    XLIV. 

_.  Three  from  7  leaves  how  many?  3  from 
17?  3  from  37?  3  from  67?  Three  from  8 
leaves  how  many  ?  3  from  88  ?  3  from  98  ?  3 
from  28  ? 

2.  Three  from  9  leaves  how  many  ?   3  from  79  ? 

3.  Three  from  ten  leaves  how  many  ?     Three 
from  twenty  ?   3  from  30  ?   3  from  40  ?  3  from  50  ? 

4.  Commencing  with   60,  give  the  numbers 
obtained  by  subtracting  3  each  time.     Thus  :  GO, 
57,  54,  51,  48,  45,  42,  39,  &c. 

5.  Twelve   things   make   a   dozen.     If   Jane 
buys  a  dozen  needles,  and  gives  away  3,  how 
many  does  she  keep?     If  she  loses  3  of  these, 
how  many  has  she  then  ? 

6.  A  boy  spends  four  cents ;  how  much  has 
he  left,  if  he  had  twelve  cents  at  first  ? 

7.  Amy  is  four  years  younger  than  Lucy,  and 
Lucy  is  13  ;  how  old  is  Amy  ? 

8.  If  there  are  eleven  persons  in  an  omnibus, 
and  three  get  out,  how  many  remain  ?     If  four 
more  get  out,  how  many  then  are  left  ? 

Eead  these  numbers.  Set  them  down  on 
your  slate.  Subtract,  and  read  the  remainders. 

(9)  .      (10)  (11)  (12)  (13) 

From  647        983         1085        4293         7658 
Tuke   434        423         1043         4131         3343 


SUBTRACTION. 


LESSON    XLV. 

Is  4  greater  or  less  than  5  ?     MM    Mil! 
Can  we  subtract  five  from  four  ? 
Can  we  subtract  five  from  five  ? 

If  we  take  five  dolls  away 
from  five  dolls,  how  many  are 
left  ?     Try  and  see. 

Whenever  we  subtract  a  number  from  itself, 
as  5  from  5,  what  is  the  remainder  ? 
Ans.  Nothing,  or  naught — 0. 

Five  marks  from  ten  marks  leave 
how  many  marks  ?     Cover  five,  and 
count  the  rest. 

Five  marks   from   twenty   marks   ^sna 
leave  how  many  marks  ? 

Five  from  thirty  leaves  how  many  ?     fjil 
5  from  40  ?     5  from  50  ?     5  from  60  ? 

James  had  6  books  on  his  table  ; 
5  have  fallen  down.  How  many 
are  left  on  the  table  ? 


^NJl 
'"H 


5  from  5  leaves  0. 
5  from  6  leaves  1. 
5  from  7  leaves  2. 
5  from  8  leaves  3. 
5  from  9  leaves  4. 


5  from  10  leaves  5. 
5  from  11  leaves  6. 
5  from  12  leaves  7. 
5  from  13  leaves  8. 
5  from  14  leaves  9. 


SUMS   IN   SUBTRACTION.  %      ^  49 


LESSON    XLVI. 





1.  Thirteen   persons    were    dining    together. 
Four  got  up  and  left ;  how  many  remained  ? 

2.  Maud  is  seven  years  old ;  her  brother  is 
five.     Which  is  the  older,  and  how  much  ? 

3.  A   man  who   had   fourteen   cents  in  his 
pocket,  gave  away  all  but  five  to  beggars.     How 
much  did  he  give  away  ? 

4.  Twelve  persons  were  standing  near  a  boiler 
which  burst.     Two  were  killed,  and  three  were 
injured ;  how  many  were  unhurt  ? 

5.  If  I  borrow  eleven  dollars,  and  payback 
four,  how  many  do  I  owe  ? 

6.  Five  from  eight  leaves  how  many  ?    5  from 
18  ?     5  from  28  ?     5  from  38  ?     5  from  48  ? 

7.  Five  from  nine  leaves  how  many  ?     5  from 
69  ?     5  from  89  ?     5  from  79  ?     5  from  99  ? 

8.  If  a  boy  who  has  thirty-seven  hens,  sells 
four,  how  many  has  he  left  ? 

9.  A  certain  boat  holds  19  persons.     If  five 
are  in  it,  how  many  empty  seats  are  there  ? 

10.  Five  from  10  leaves  how  many  ?   5  from  5  ? 

SUMS   FOR   THE    SLATE. 

(1)  (2)  (3)  (4)  (5) 

From  937    8165    4397    6028    5984 
Take  425    5054    2154    4014    5234 


50 


SUBTRACTION. 


LESSON    XLVII. 

What  is  the   smallest   number  that  we  can 
subtract  6  from  ? 

How  many  does  6  from  6  leave  ? 

Look  at  these  seven  mice.  Six 
are  running  away ;  how  many 
remain  ? 

Six  from  7  leaves  how  many?     6  from  17? 
6  from  27  ?     6  from  47  ?     6  from  67  ? 

This  wheel  has  eight  spokes.  Six  of 
them  are  whole  ;  how  many  are  broken  ? 
Count  and  see.  | 

Six  from  8  leaves  how  many  ?     6  from  38  ? 
6  from  58  ?     6  from  78  ?     6  from  98  ? 

Take  six  forks  away  from  nine 
forks,  and  how  many  are  left  ? 

•/HHHc   •/HHHHHc    Six  stars  from  ten 
stars  leave  how  many  stars  ? 

1  1  j  !  1    1  I  I  I  I  I     Six  marks  from  eleven  marks 
leave  how  many  marks  ? 


6  from     6  leaves  0. 

6  from     7  leaves  1. 

6  from     8  leaves  2. 

6  from     9  leaves  3. 

6  from  10  leaves  4. 


6  from  11  leaves  5 

6  from  12  leaves  6. 

6  from  13  leaves  7 

6  from  14  leaves  8 

6  from  15  leaves  9. 


SUBTRACTION.  51 


LESSON    XLVIII. 

What  is  Subtraction  ?  What  is  the  answer 
called  in  a  sum  in  Subtraction  ? 

What  is  the  smallest  number  that  we  can 
subtract  7  from  ? 

How  many  does  seven  from  seven  leave  ?  7 
from  27  ?  7  from  97  ?  7  from  57  ?  7  from  37  ? 

Eight  fingers  on  two  hands.     If 
seven  of  them  are  held  up  straight, 
how  many  will  be  bent  down  ? 
How  many  does  seven  from  eight  leave  ?     7 
from  18  ?     7  from  88  ?     7  from  68  ?     7  from  48  ? 
7  from  58  ? 

Here  we  have  nine  rings 
on  a  string.  If  you  cover 
7  with  your  hand,  how  many  will  you  see  ? 

Seven  from  9  leaves  how  many  ?     7  from  79  ? 

Ten  bees  are  flying  round  a  hive. 
If  7  are  on  one  side,  how  many  are 
on  the  other  ?     Count  and  see. 
Seven  from  ten  leaves  how  many  ? 


7  from     7  leaves  0. 

7  from     8  leaves  1. 

7  from     9  leaves  2. 

7  from  10  leaves  3. 

7  from  11  leaves  4. 


7  from  12  leaves  5. 

7  from  13  leaves  6. 

7  from  14  leaves  7. 

7  from  15  leaves  8. 

7  from  16  leaves  9. 


52  SUMS    IN    SUBTRACTION. 

LESSON    XLIX. 

1.  There  were  thirteen  lights  in  a  street.     Six 
are  blown  out ;  how  many  are  left  burning? 

2.  Plenry    broke    7    teeth   out    of    a   comb. 
How  many  teeth  were  left,  if  there  were  27  at 
first? 

3.  How  many  sugar-plums  would  you  have 
to  put  with  nine,  in  order  to  make  fifteen  ? 

4:.  If  a  boy  has  eleven  almonds,  and  eats  all 
but  seven,  how  many  does  he  eat  ? 

5.  A  blind  man  received  eight  cents  from  one 
kind  boy,  and  four  from  another.  If  he  spent 
six  cents  on  his  way  home,  how  many  had  he 
left? 

SUMS   FOR   THE    SLATE. 

1.  From  ninety-seven  subtract  seventy-six. 

2.  Take   six    thousand   and   seventeen    from 
eight  thousand  three  hundred  and  forty-eight  ? 

3.  From  five  thousand  and  seventy -two  take 
three  thousand  and  twenty-two. 

4.  A  man  having  ninety-one  dollars,  bought 
a  coat  for  twenty  dollars  ;  how  much  had  he  left? 

5.  A  ship  with  six  hundred  and  sixty-nine 
passengers  on  board  was  wrecked.     Four  hundred 
and  sixteen  escaped ;  how  many  were  lost  ? 

6.  A  gale   swept  over  a  garden   containing 
eighty-seven  bean-poles.     Seventy-six  were  blown 
down  ;  how  many  remained  standing  ? 


SUBTRACTION. 


53 


LESSON    L. 

What  is  the  smallest  number  that  we  can  take 
8  from  ? 

How  many  does  eight  from  eight  leave  ?     8 
from  108  ?     8  from  68  ?     8  from  18  ?     8  from  58  ? 
Nine  marbles  were  placed  in  the 
centre  of  a  ring.     The  first  boy  that 
shot,  drove  eight  away  from  the  cen- 
tre ;  how  many  were  left  there  ? 
8  from  9  leaves  how  many?     8  from  29?  .  8 
from  99  ? 

Ten  trees  were  set  out  thus.     If    •     •     •     • 
8   afterwards  died,  how  many  re-       ®  • 

mained  ?     Cover  8  over,  and  count     ©     o     ©     o 
8  from  10  leaves  —  . 


the  rest. 


Eleven   spiders   were  on  a  wall, 
but  eiht  have  crawled  down.   How 


many   remain  there? 

leaves  how  many  ? 
Take   eight  rings   away  from 
twelve  rings,  and  how  many  will 
be  left? 


8    from    11 


oo 

00 


0000 
0000 


from  8  leaves  0. 

from  9  leaves  1. 

from  10  leaves  2. 

from  11 

from  12 


leaves  3. 
leaves  4. 


8  from  13  leaves  5. 
8  from  14  leaves  6. 
8  from  15  leaves  7. 
8  from  16  leaves  8. 
8  from  17  leaves  9. 


54  SUBTR  ACTION. 


LESSON     LI. 


A 

ama 

Here  is  a  frame  with  wires  stretched  across 
it,  and  each  wire  runs  through  balls. 

Count  the  balls  on  the  top  wire.  How  many 
are  there  in  all  ?  Now,  if  from  these  10  balls, 
we  push  away  9  to  the  right,  how  many  are  left  ? 

How  many  balls  on  the  second  wire  ?  Push 
away  9,  and  how  many  are  left  ? 

How  many  balls,  on  the  third  wire?  Cover 
9  with  your  finger,  and  how  many  do  you  see  ? 

How  many  balls  on  the  fourth  wire  ?  Cover 
9  over,  and  how  many  can  you  count  ? 

How  many  balls  on  the  fifth  wire  ?  Cover 
9  over,  and  how  many  are  left  ? 


9  from  9  leaves  0. 
9  from  10  leaves  1. 
9  from  11  leaves  2. 
9  from  12  leaves  3. 
9  from  13  leaves  4. 


9  from  14  leaves  5. 

9  from  15  leaves  6. 

9  from  16  leaves  7. 

9  from  17  leaves  8. 

9  from  18  leaves  9. 


SUMS   IN    SUBTK ACTION.  55 


LESSON   LII. 

1.  A  jar  of  lard  weighed  seventeen  pounds. 
If  the  jar  weighed  eight  pounds,  what  was  the 
weight  of  the  lard  ? 

2.  I  bought  a  dozen  eggs,  but  eight  of  them 
were  bad.     How  many  were  good  ? 

3.  Sixteen  boys  went  a  skating.     If  nine  of 
them  fell  on  the  ice,  how  many  escaped  falling  ? 

4.  A  farmer  had  eighteen  cows.     Four   of 
them  died,  and  he  sold  five  ;  how  many  were  left? 

5.  Nine  lemons  fell  from  a  tree   on  which 
thirteen  were  growing.     HQW  many  remained  ? 

6.  A  fisherman  who  had  seventeen  lobsters, 
sold  six  in  the  morning  and  two  in  the  afternoon. 
How  many  had  he  left  ? 

7.  A  boy  having  fourteen  dollars  in  the  bank, 
drew  out  all  but  eight.     How  much  did  he  draw 
out? 

SUMS    FOE    THE   SLATE. 
(1)  (2)  (3)  (4)  (5) 

From  18    873    5268    9145    8460 
Take  9    721    1045    8043    6250 


(6)       (7)        (8)        (9)        (10) 

From  17    921    2397    5679    4396 
Take  8    721    1163    4645    3291 


56  CARRYING   IN    SUBTRACTION. 


LESSON    LIU. 

From       652 
Take        379 


Look  at  this  sum.  The  lower  number  is  the 
smaller.  Hence  it  can  be  taken  from  the  upper. 

Always  begin  to  subtract  at  the  right. 

9  from  2. — We  can  not  take  9  from  2,  because 
9  is  greater  than  2.  So  we  add  10  to  the  2, 
making  it  12.  9  from  12  leaves  3.  Set  down  3 
for  the  first  figure  of  the  remainder. 

Now,  to  balance  the  10  units  just  added  to  3 
in  the  upper  line,  add  1  ten  to  the  7  tens  in  the 
lower  line, — making  8.  Subtract  8. 

8  from  5. — We  can  not  take  8  from  5.  So 
add  10  to  the  5,  making  it  15.  8  from  15  leaves 
7.  Set  down  7  for  the  second  figure  of  the  re- 
mainder. 

To  balance  the  10  just  added  to  the  5  tens  in 
the  upper  line,  add  1  hundred  to  the  3  hundreds 
in  the  lower  line, — making  4.  Subtract  4. 

4  from  6  leaves  2.  Set  down  2  for  the  third 
figure  of  the  remainder.  Answer,  273. 

This  process  is  called  Carrying. 

RULE   FOR   CARRYING   IN    SUBTRACTION. When 

the  lower  figure  is  greater  than  the  one  above  it, 
add  10  to  the  upper  figure,  subtract,  and  carry  1 
to  the  next  lower  figure. 


SUMS   IN   SUBTRACTION.  57 


LESSON    LIV. 

SUMS   FOE*  THE    SLATE. 

(1)  (2)  (3)  (4)  (5) 

From  752    8364:    9017    3429    8560 
Take  479    2192    4108    3173    6936 


(6)  (7)  (8)  (9)  (10) 

From  416        5832        7411         8267         6059 
Take  273         1988        4143         3179         3421 


11.  There  were  seven  hundred  and  five  fish 
in  a  net.     But,  in  drawing  the  net,  ninety-six 
were  lost ;  how  many  fish  were  caught  ? 

12.  Charles  bought  some  meat  for  thirty-nine 
cents.     He  gave  the  butcher  half  a  dollar  (worth 
fifty  cents).     How  much  change  did  he  get  ? 

13.  A  man  who  had  four  thousand  and  ten 
dollars,  gave  his  son  two  thousand  seven  hundred 
and  eight  dollars.     How  much  did  he  keep  ? 

14.  A  farmer  sold  eight  hundred  and  twenty- 
five  acres  of  land.     How  many  had  he  left,  if  his 
farm  contained  a  thousand  acres  at  first  ? 

15.  Fanny  had  a  present  of  a  box  containing 
144  pens.     If  she  used  thirty-nine  of  them  in  a 
month,  how  many  had  she  left  ? 

16.  A  drover  sold  87  head  of  cattle  out  of  a 
drove  of  250.     How  many  had  he  left? 


58  SUMS    IN    SUBTRACTION. 

LESSON    LV. 

' 
MENTAL   EXERCISES. 

1.  A  car  started  with  40  passengers.     At  the  | 
first  station,  10  passengers  got  off  and  3  got  on. 
How  many  did  it  then  contain  ? 

2.  A  rose-bush  had  82  roses  on  it.     The  next 
day,  6  of  these  roses  fell  to  pieces,  and  9  new  ones 
opened.     How  many  were  then  on  the  bush  ? 

3.  Leaving  home  with  a  hundred  dollars  in 
my  purse,  I  spent  five  for  a  vest,  five  for  a  coat, 
and  five  for  boots.     How  much  had  I  left  ? 

4.  Said  Dick  to  Stephen,  "  Give  me  your  nine 
chickens,  and  I  shall  have  seventy-eight."     How 
many  chickens  had  Dick  ? 

5.  A  man  rode  90  miles  in  4  days.     The  first 
day  he  went  70  miles  ;  the  second  day,  10 ;  the 
third  day,  5.     How  far  did  he  go  the  fourth  day  ? 

6.  Subtract  the  sum  of  70, 10,  and  5,  from  90. 

7.  If  Julia  is  twenty-three  years  old,  and  her 
brother  is  twenty-nine,  what  is  the  difference  in 
their  ages  ? 

8.  Six,  and  five,  and  nine,  and  how  many 
more,  make  twenty-eight  ? 

9.  A  man  who  had  twenty  cents,  met  five  poor 
boys,  and  gave  them  each   three  cents.     How 
many  cents  had  he  left  ? 

10.  From  20  take  the  sum  of  3,  3,  3,  3,  and  3. 


MULTIPLICATION.  59 

LESSON   LVI. 

One  bird,  taken  once,  is  one  bird. 

If  we  take  one  bird  twice,  we 
have  two  birds. 

If  we  take  two  birds  once,  we 
have  two  birds. 

If  we  take  two  birds 
twice,  how  many  birds 
have  we  ?^ 

What  is  taking  a  number  one  or  more  times 
called  ? 

Ans.  Multiplying. 

Taking  a  number  once  is  multiplying  by  1. 
Taking  a  number  twice  is  multiplying  by  2. 
Taking  a  number  3  times  is  multiplying  by  3. 

Multiplying  is  a  short  way  of  doing  what  ? 
Ans.  Of  adding  a  number  to  itself.     Thus  : — 

Twice  1  is  2.  1  and  1  are  2. 

Three  times  1  is  3.  1  and  1  and  1  are  3. 

When  we  multiply,  what  is  the  result  called  ? 
Ans.  The  Product.     When  we  say  Twice  one 
is  two,  2  is  the  product. 

What  is  Multiplication  ? 
Ans.  Multiplication  is  the  process  of  taking  a 
number  a  certain  number  of  times. 


60  MULTIPLICATION. 


LESSON    LVII. 

What  does  once  mean  ? 
Ans.  Once  means  one  time. 

One  acorn,  taken  once,  is  one  acorn. 
'Once  1  is  1.  If  1  is  multiplied  by  1,  the 
product  is  1. 

Two  acorns,  taken  once,  are  two 
acorns.  Once  2  is  2.  If  2  is  multi- 
plied by  1,  what  is  the  product  ? 

-/HHr  How  many  do  three  stars,  taken  once, 
make  ?  How  much  is  once  3  ?  If  3  is  multiplied 
by  1,  what  is  the  product  ? 

How  many  do  four  eggs,  taken 
once,  make  ?  How  much  is  once  4  ? 
If  4  is  multiplied  by  1,  what  is  the 
product  ? 

Then,  Once  1  is  1.  Once  2  is  2.  Once  3  is 
3.  Once  4  is  4.  Once  any  number  is  the  number 
itself. 

Learn  the  Table  forward  and  backward. 


Once 
Once 
Once 
Once 
Once 

1 

2 
3 
4 

5 

is 
is 
is 
is 
is 

1. 

2. 

4:. 
D. 

Once 
Once 
Once 
Once 
Once 

6 

7 
8 
9 
10 

is 
is 
is 
is 
is 

6. 
7. 
8. 
9. 
10. 

MULTIPLICATION. 


61 


LESSON    LVIII. 
SUMS     FOK     THE     SLATE. 


(1) 

Multiply       98 
By  1 


(2) 

150 
1 


(3)  (4) 

742        3018 
1  1 


(5) 

6932 
1 


What  does  twice  mean  ?         Ans.  Two  times. 
If  we  take  one  bird  twice,  how 
>many  birds  have  we?     How  much 
is  twice  1  ? 
If  we  take  two  birds 
twice,  how  many  birds 
have  we  ?     How  much  is  twice  2  ? 

•/HHr       If  we  take  three  stars  twice,  how  many 
•>HKr    stars  have  we?     How  much  is  twice  3 ? 

What  is  the  same  as  multiplying  a  number 
by  2? 

Ans.  Adding  the  number  to  itself. 
Twice  1  is  2.  1  and  1  are  2. 

Twice  2  is  4.  2  and  2  are  4. 


Twice  1  is     2. 
Twice  2  is     4. 
Twice  3  is     6. 
Twice  4  is     8. 
Twice  5  is  10. 

Twice     6  is  12. 
Twice     7  is  14. 
Twice     8  is  16. 
Twice     9  is  18. 
Twice  10  is  20. 

62  MULTIPLICATION. 


LESSON    LIX. 

0,  taken  any  number  of  times,  is  still  0. 
Twice  0  is  0.     3  times  0  is  0.     4  times  0  is  0. 

"Now  you  have  some  sums  for  the  slate.   Read 
the  numbers  multiplied,  and  the  products. 

(1)  (2)  (3)  (4)  (5) 

Multiply  34        121         520        4213        3004 

By  2  2  2  2  2 


6.  How  much  is  twice  four  hundred  and  three  ? 

7.  Multiply  two  thousand  one  hundred  and 
eleven  by  two. 

8.  If  two  thousand  three  hundred  and  forty- 
one  is  multiplied  by  two,  what  is  the  product  ? 

9.  How  much  is  once  seventy-six  ? 

10.  Multiply  four  thousand  and  thirteen  by  2. 

11.  What  is  the  product  of  one  and  two  thou- 
sand seven  hundred  ? 

12.  How  much  is  twice  five  hundred  and 
thirty-two  ? 

13.  Multiply  twelve  hundred  by  two. 


3  times  1  is  3. 
3  times  2  is  6. 
3  times  3  is  9. 
3  times  4  is  12. 
3  times  5  is  15. 


3  times  6  is  18. 
3  times-  7  is  21. 
3  times  8  is  24. 
3  times  9  is  27. 
3  times  10  is  30. 


MULTIPLICATION.  63 


LESSON    LX. 

1.  If  a  cord  of  wood  costs  five  dollars,  what 
will  three  cords  cost  ? 

MODEL. — If  1  cord  costs  5  dollars,  3  cords  will  cost  3 
times  5  dollars,  or  15  dollars.  Answer,  15  dollars. 

Do  all  the  mental  suras  in  Multiplication  according  to 
this  model. 

2.  What  will  two  books  cost,  at  a  dollar  each  ? 

3.  How  much  will  a  clerk,  who  gets  eight 
dollars  a  week,  earn  in  three  weeks  ? 

4.  At  10  dollars  each,  what  will  2  desks  cost  ? 

5.  A  man  gave  two  beggars  nine  cents  apiece ; 
how  much  did  he  give  them  both  ? 

6.  If  one  woman  can  make  three  dresses  in  a 
week,  how  many  dresses  can  three  women  make  ? 

7.  I  have  two  classes,  .each  containing  seven 
boys  ;  how  many  boys  do  both  contain? 

8.  If  a  barrel  of  flour  lasts  a  family  nine  weeks, 
how  long  will  three  barrels  last  them  ? 

9.  When  oranges  are  worth  two  cents  apiece, 
and  lemons  one  cent,  what  will  I  have  to  pay  for 
three'  oranges  and  two  lemons  ? 


4  times  1  is  4. 
4  times  2  is  8. 
4  times  3  is  12. 
4  times  4  is  16. 
4  times  5  is  20. 


4  times  6  is  24. 
4  times  7  is  28. 
4  times  8  is  32. 
4  times  9  is  36. 
4  times  10  is  40. 


64 


MULTIPLICATION. 


LESSON    LSI. 

If  one  girl  can  pick  five 
quarts  of  berries  in  a  morn- 
ing, how  many  quarts  can 
four  girls  pick  ? 

MODEL. — If  1  girl  can  pick  5 
quarts,  4  girls  can  pick  four  times 
quarts,  or  20  quarts.     Answer,  20  quarts. 

2.  There  are  four  fingers  on  one  hand ;  how 
many  are  there  on  four  hands  ? 

3.  How  many  days  are  there  in  four  weeks, 
there  being  seven  days  in  one  week  ? 

4.  "What  will  4  combs  cost,  at  10  cents  apiece  ? 

5.  If  one  horse  eats  8  quarts  of  oats  in  a  day, 
how  much  will  4  horses  eat  at  the  same  rate  ? 

6.  A  father  gave  each  of  his  4  sons  3  dollars  ; 
how  much  did  he  give  them  in  all  ? 

7.  If  one  stage  holds  9  men,  how  many  men 
will  4  such  stages  hold  ? 

Commencing  with  5,  give  the  numbers  formed 
by  adding  5  each  time.  Thus :  5,  10,  15,  20,  25, 
30,  &c. 


5  times  1  is  5. 
5  times  2  is  10. 
5  times  3  is  15. 
5  times  4  is  20. 
5  times  5  is  25. 


5  times 
5  times 
5  times 
5  times 


6  is  30. 

7  is  35. 

8  is  40. 

9  is  45. 


5  times  10  is  50. 


MULTIPLICATION.  65 

LESSON    LXII. 

How  much  is  5  times  4?  How  much  is  4 
times  5?  Which  is  the  greater? 

How  much  is  5  times  3  ?  How  much  is  3 
times  5  ?  Which  is  the  greater  ? 

In  finding  the  product  of  two  numbers,  does 
it  matter  which  we  multiply  by  ? 

1.  How  many  miles  will  a  horse  trot  in  5 
hours,  if  he  trots  10  miles  an  hour  ? 

2.  If  Henry  reads  5  books  every  week,  how 
many  will  he  read  in  5  weeks  ? 

3.  What  are  5  pounds  of  pork  worth,  at  9 
cents  a  pound  ? 

4.  How  many  trees  are  there  in  5  rows,  con- 
taining 6  trees  each? 

5.  Louise  writes   2  pages  every  day ;    how 
many  pages  does  she  write  in  5  days  ? 

6.  There  are  5  cages  in  the  Museum,  with  8 
monkeys  in  each  ;  how  many  monkeys  in  all  ? 

7.  Ned  went  5  times  to  the  station,  and  took 
1  letter  each  time  ;  how  many  did  he  take  in  all  ? 


6  times  1  is     6. 
6  times  2  is  12. 
6  times  3  is  18. 
6  times  4  is  24. 
6  times  5  is  80. 

•  6  times     6  is  36. 
6  times     7  is  42. 
6  times     8  is  48. 
6  times     9  is  54. 
6  times  10  is  60. 

66  MULTIPLICATION. 


LESSON    L2III, 

How  much  is  6  times  2  ?     How  much  is  twice 
6  ?     Which  is  greater  ? 

Which  is  greater,  6  times  4  or  5  times  5  ? 
Which  is  greater,  6  times  2  or  3  times  4  ? 

1.  Walking  three  miles  an  hour,  how  far  will 
a  man  go  in  six  hours  ? 

2.  If  one  box  of  tea  lasts  a  family  six  months, 
how  long  will  six  boxes  last  them  ? 

3.  How  many  dollars  are  there  in  six  bags, 
containing  seven  dollars  each  ? 

4.  One  eagle  is  worth  ten  dollars.   How  many 
dollars  are  six  eagles  worth  ? 

5.  How  far  will  we  get  from  Albany,  sailing 
6  hours  in  a  boat  that  goes  9  miles  an  hour  ? 

6.  Jane  and  her  five  sisters  have  each  a  canary 
bird.     How  many  birds  have  they  all  ? 

7.  How  many  flowers  are  there  in  6  nosegays, 
if  each  contains  8  flowers  ? 

8.  Six  pin-cushions,  with  five  pins  in  each, 
will  contain  how  many  pins  in  all  ? 


7  times  1  is  7. 
7  times  2  is  14. 
7  times  3  is  21. 
7  times  4  is  28. 
7  times  5  is  35. 


7  times  6  is  42. 
7  times  7  is  49. 
7  times  8  is  56. 
7  times  9  is  63. 
7  times  10  is  70. 


MULTIPLICATION.  67 


LESSON    LXIV. 

How  much  is  7  times  6  ?  How  much  is  6 
times  7  ?  Which  is  the  greater  ? 

How  many  times  7  is  equal  to  7  times  3  ? 

Ans.  3  times  7.     Both  make  21. 

What  is  equal  to  7  times  5  ?    To  7  times  4  ? 

1.  How  many  panes  of  glass  are  there  in  7 
windows,  containing  8  panes  each  ? 

MODEL. — If  there  are  8  panes  in  1  window,  in  7  windows 
there  will  be  7  times  8  panes,  or  56  panes.  Answer,  56 
panes. 

2.  If  a  boy  spends  four  cents  a  day,  how  much 
will  he  spend  in  a  week,  which  contains  7  days? 

3.  One  fly  has  two  wings  ;  how  many  wings 
have  seven  flies  ? 

4.  What  will  7  rings  cost,  at  9  dollars  each  ? 

5.  How  many  sums  will  Ella  do  in  seven  days, 
if  she  does  seven  every  day  ? 

6.  How  many  dollars  in  seven  eagles,  allow- 
ing ten  dollars  to  the  eagle  ? 

7.  How  many  boats  pass  a  draw-bridge  in  7 
days,  if  five  boats  go  through  each  day  ? 


8  times  1  is  8. 
8  times  2  is  16. 
8  times  3  is  24. 
8  times  4  is  32. 
8  times  5  is  40. 


8  times  6  is  48. 
8  times  7  is  56. 
8  times  8  is  64. 
8  times  9  is  72. 
8  times  10  is  80. 


68 


MULTIPLICATION. 


LESSON    LXV. 


1.  If  these  boys  skate  four  miles  an  hour,  how 
many  miles  will  they  skate  in  8  hours  ? 

2.  Twice  every  day  Fred  and  Frank  come 
with  their  sleds,  to  ride  down  hill.     How  many 
times  do  they  come  in  eight  days  ? 

3.  If  it  takes  3  hours  to  cut  a  ton  of  ice  from 
the  pond,  how  long  will  it  take  to  cut  8  tons  ? 

4.  One  day  8  sleigh-loads,  of  9  persons  each, 
came  to  the  pond  ;  how  many  persons  was  that  ? 

5.  What  will  eight  loads  of  evergreens  cost, 
at  six  dollars  a  load  ? 


9  times  1  is     9. 

9  times  2  .is  18. 
9  times  3  is  27. 
9  times  4  is  36. 
9  times  5  is  45. 


9  times  6  is  54. 
9  times  7  is  63. 
9  times  8  is  72. 
9  times  9  is  81. 
9  times  10  is  90. 


MULTIPLICATION.  69 


LESSON    LXVI. 

(1)  (2)  (3)  (4)  (5)  (6) 

Multiply    4:1  21  90  81  70  621 

BJ  567894 


205  2484 

7.  Which  is  greater,  9  times  4  or  7  times  5  ? 

8.  How  many  legs  has  one  chair  ?     How  many 
legs,  then,  will  nine  chairs  have  ? 

9.  How  many  fingers  has  one  boy?     How 
many  fingers,  then,  will  nine  boys  have  ? 

10.  Ada's  father  gives  her  and  her  8  brothers 
6  cents  each.     How  much  does  he  give  them  all  ? 

11.  I  have  five  hens,  and  each  hen  has  nine 
chickens.     Hens  and  chickens,  how  many  have  I  ? 

12.  How  much  will  nine  turkeys  weigh,  if 
their  weight  is  eight  pounds  apiece  ? 

13.  There  are  nine  chains,  each  six  feet  long. 
What  is  the  length  of  the  whole  nine  ? 

14.  How  many  gallons  in  9  ten-gallon  casks  ? 

Eepeat  the  even  tens :  10,  20,  30,  40,  50,  &c. 


10  times  1  is  10. 
10  times  2  is  20. 
10  times  3  is  30. 
10  times  4  is  40. 
10  times  5  is  50. 

10  times     6  is     60. 
10  times    7  is    70. 
10  times     8  is     80. 
10  times    9  is     90. 
10  times  10  is  100. 

70  MULTIPLICATION. 


LESSON    LXVII. 

1         2  What  is  an  easy  way  of  multiply- 

10       10       ing  a  number  by  10  ? 
10       20  Ans.  Placing  a  naught  after  it  ? 

1.  Set  down  these  numbers;  multiply  them 
by  10  in  the  way  just  shown  : — 

Eight  hundred  and  forty-seven. 
Six  hundred  and  seventy-nine. 
Two  hundred  and  thirteen. 
Seven  hundred  and  five. 
Thirty-three.     Nineteen.     Fifty-one. 

2.  Ten  cents  make  a  dime  ;  ten  dimes  make  a 
dollar.      How   many  cents,   then,  in   a   dollar  ? 
How  many  cents  are  seven  dimes  worth  ? 

3.  If  you  can  buy  two  apples  for  a  cent,  how 
many  can  you  get  for  ten  cents  ? 

4.  Ann  is  five  years  old.     If  she  lives  to  be 
ten  times  as  old,  what  will  be  her  age? 

5.  How  many  quarts  will  ten  jars  contain,  if 
each  holds  three  quarts  ? 

6.  At  3  cents  each,  what  will  10  oranges  cost  ? 

7.  There  are  nine  inches  in  a  quarter  of  a 
yard;  how  many  inches  in  ten  quarters? 

8.  If  for  ten  days  you  get  four  good  marks 
each  day,  how  many  do  you  get  in  all  ? 

Review  all  the  Tables,  from  page  60,  till  you 
can  say  them  perfectly. 


CARRYING   IN   MULTIPLICATION.  71 


LESSON    LXVIII. 

Multiply       734: 
By  6 


Look  at  this  sum.  Always  begin  to  multiply 
at  the  right. 

6  times  4  is  24 — 4  units  and  2  tens.  Set 
down  the  4  units  in  the  units'  place,  and  carry 
the  2  tens  to  the  next  product. 

6  times  3  is  18,  and  the  2  tens  carried  make 
20  tens — or  2  hundreds.  Set  down  0  in  the  tens' 
place,  and  carry  2  hundreds  to  the  next  product. 

&  times  7  is  42,  and  the  2  carried  makes  44. 
Answer,  4404. 

When  must  we  carry  in  Multiplication  ? 
Ans.  Whenever  we  obtain  a  product  over  9. 

What  is  the  rule  for  carrying  ? 

Ans.  Set  down  the  right-hand  figure,  and 
carry  the  left-hand  figure  to  the  next  product. 

If  36  is  your  product,  which  figure  do  you 
set  down,  and  which  do  you  carry  ?  If  63  ?  If  72  ? 

Do  the  following  sums  aloud,  just  as  the  ex- 
ample at  the  top  of  the  page  is  done : — 

Multiply     863  638  742  914 

By  4  5  7  9 

3452    3190    5194    8226 


72 

MISCELLANEOUS    SUMS. 

LESSON    LXIX. 

What  is  Numeration  ?     "What  is  Notation  ? 
What  is  Addition  ?     What  is   Subtraction  ? 
What  is  Multiplication  ? 

SUMS   FOR  THE   SLATE. 

(1) 

(2) 

(3) 

(4) 

(5) 

Add    987 

846 

869 

1752 

789 

236 

155 

456 

990 

2789 

795 

383 

978 

2671 

789 

121 

353 

519 

2532 

2789 

143 

625 

780 

898 

1789 

422 

831 

659 

1098 

339 

(6) 

(7) 

(8) 

(9) 

(10) 

From      96 

410 

863 

1002 

3507 

Take       38 

307 

264 

109 

1238 

(11)             (12) 

(13) 

(14) 

(15) 

Multiply 

81        72 

39 

160 

263 

By 

3           6 

2 

8 

4 

(16)             (17) 

(18) 

(19) 

(20) 

Multiply 

72        90 

85 

698 

549 

By 

5         10 

7 

10 

9 

MISCELLANEOUS    SUMS.  73 

LESSON    LXX 

"What  is  the  result,  or  answer,  called  in  Ad- 
dition ?  "What,  in  Subtraction  ?  What,  in  Mul- 
tiplication ? 

1.  What  is  the  sum  of  four  hundred  and  sixty- 
one,  five  hundred    and  eighty-four,  and  seven 
hundred  and  two  ? 

2.  What  is  the  product  of  eight  hundred  and 
seventy -two,  and  nine  ? 

3.  If  forty-six  is  taken  from  eight  thousand 
and  twenty-nine,  what  is  the  remainder  ? 

4.  How  many  pages  in  nine  books,  if  each 
book  has  two  hundred  and  eighty-eight  pages? 

5.  One  book  has  four  hundred  and  fifty  pages ; 
another  has  two  hundred  and  sixty-four.     How 
many  pages  have  both  books  together?     How 
many  more  pages  has  one  than  the  other  ? 

6.  If  a  man  reads  forty -nine  books  every  year, 
how  many  will  he  read  in  ten  years  ? 

7.  A  gardener  set  out  a  hundred  and  nineteen 
trees  every  week  for  five  weeks.     If  95  out  of 
the  whole  number  died,  how  many  lived  ? 

8.  Maud's  uncle  left  his  whole  property  to 
her  and  her  five  brothers,  giving  them  each  one 
thousand  and  fifty  dollars.     What  was  he  worth 
in  all? 

9.  Multiply  a  thousand  and  twelve  by  eight. 


74  MULTIPLYING   BY   TWO   FIGURES. 


LESSON     LXXI. 

Multiply  509  by  18.     Let  us  see  how 
509       we  are  to  multiply  by  two  figures. 

Set  down  18  under  509,  units  under 


4072       units,  tens  under  tens. 
509  Begin  at  the  right.    • 

9162  8  times  9  is  72.     Set  down  2,  and 

carry  7. 

8  times  0  is  0,  and  7  is  7.     Set  it  down. 

8  times  5  is  40.  Set  it  down.  The  first 
product,  as  you  see  in  the  sum,  is  4072. 

Now  multiply  by  1. 

Once  9  is  9.  Set  it  down  in  the  same  column 
with  the  1  by  which  you  are  multiplying.  Once 
0  is  0.  Once  5  is  5.  The  second  product  is  509. 

Now  add  the  two  products.     Answer,  9162. 

Always  set  the  first  figure  of  each  product  in 
the  same  column  with  the  figure  by  which  you  are 
multiplying. 

In  finding  the  product  of  two  numbers,  multi- 
ply by  the  one  that  has  the  fewer  figures. 

Do  these  sums  aloud,  like  the  one  above : — 

Multiply        87  260  159 

By  24  38  56 


348  2080  954 

174  780  795 


Product     2088  9880  8904 


MULTIPLICATION.  75 

LESSON  LXXII. 

When  0  occurs  in  the  number  you  multiply 
by,  how  do  you  proceed  ? 

Ans.  Bring  down  the  0,  and  go  on  multiply- 
ing by  the  next  figure,  all  in  the  same  line. 

Multiply  97  by  30.  97 

Bring  down  the  0.  Then  multiply  ^0 
by  3,  setting  the  result  in  the  same  line.  2910 

3  times  7  is  21.     Set  down  1  under 
the  3,  and  carry  2.     3  times  9  is  27,  and  2  is 
29.     Answer,  2910. 

What  is  an  easy  way  of  multiplying  a  number 
by  100? 

Ans.  Placing  two  naughts  after  it. 

How  much  does  57  multiplied  by  100  make  ? 

Multiply  19  by  100.  Multiply  100  by  19. 
Which  is  the  greater  ? 

What  is  the  product  of  65  and  100  ? 

SUMS   FOR    THE    SLATE. 
(1)  (2)  (3)  (4)  (5) 

Multiply  27        81         90          98        190 
By         16        37        24:          95          26 


(6)  (7)  (8)  (9)  (10) 

Multiply  34:        57        68          90          43 
By         20         89         50         100         100 


76 


DIVISION. 


LESSON    LXXIII. 

Two  oxen  make  a  yoke.    How 
many  yoke  will  4  oxen  make  ? 

Ans.  As  many  yoke  as  2  is  contained  times 
in  4, — or  2.  Answer,  2  yoke. 

How  many  yoke  will  6 
oxen  make  ? 
Ans.  As  many  yoke  as  2  is  contained  times 
in  6, — or  3.     Answer,  3  yoke. 

"What  is  finding  how  many  times  one  number 
is  contained  in  another  called  ? 

Ans.  Dividing.  Finding  how  many  times  2 
is  contained  in  6,  is  dividing  6  by  2. 

What  is  meant  by  dividing  9  by  3  ? 

Ans.  Finding  how  many  times  3  is  contained 
in  9. 

"When  we  divide,  what  is  the  result  called  ? 

Ans.  The  Quotient.  Two  is  contained  in  6 
three  times  ;  3  is  the  quotient. 

When  we  divide  by  1,  what  is  the  quotient. 

Ans.  The  same  as  the  number  divided. 
Thus  :— 


1  in  1,  once. 
1  in  2,  twice. 
1  in  3,  3  times. 
1  in  4,  4  times. 
1  in  5,  5  times. 


in 
in 
in 
in 


9, 


6  times, 

7  times. 

8  times. 

9  times. 


I     1  in  10,  10  times. 


DIVISION. 


77 


LESSON    LXXIV. 

What  is  Division  ? 

Ans.  Division  is  the  process  of  finding  how 
many  times  one  number  is  contained  in  another. 

What  is  the  result  called  in  Division  ? 

How  many  times  is  one  apple  contained  in 
one  apple  ?  In  five  apples  ?  In  ten  ?  In  four- 
teen? In  a  hundred  apples?  In  a  thousand 
apples  ? 

How  many  times  will  1  go  into  3  ?     Into  27  ? 

Divide  415  by  1,  and  what  is  the  quotient  ? 

How  many  times  is  2  contained  in  4  ?     In  6  ? 
Two  make  a  pair.     How  many  pair  will  8 
rabbits  make  ?     Count  and  see. 


How  many  pair  will  ten  horses  make 


2  in 
2  in 
2  in 
2  in 


2,  once. 
4,  twice. 

3  times. 

4  times. 


6, 
8, 


2  in  10,  5  times. 


2  in  12,  '6  times. 
2  in  14,  7  times. 
2  in  16,  8  times. 
2  in  18,  9  times. 
2  in  20,  10  times. 


78  DIVISION. 


LESSON    LXXV. 

1.  Two  make  a  brace.     If  a  sportsman  shoots 
20  pheasants,  how  many  brace  does  that  make  ? 

MODEL.— It  makes  as  many  brace  as  2  is  contained  times 
in  20, — or  10.     Answer,  10  brace. 

Follow  this  model  in  the  mental  sums  in  Division. 

2.  Two  make  a  couple.     If  a  group  of  16 
boys  pair  off,  how  many  couples  will  they  make? 

3.  How  many  pair  will  twelve  gloves  make  ? 

4.  If  16  cents  are  divided  equally  between 
two  poor  men,  how  many  cents  will  each  get? 

5.  Amy  and  her  sister  divided  14  chestnuts 
equally  between   them.     How  many  did  Amy 
have  ? 

^^rt!L*«£x         When  a  thing  is  divided  into 
two  equal  parts,  each  part  is  called 

What  is  the  half  of  14  ?     Of  18 '? 

How  many  times  is  1  contained  in  1  ?   2  in  2  ? 
When  we  divide  any  number  by  itself,  what  is 
the  quotient?  Ans.  1. 

How  many  times  is  3  contained  in  3  ? 


3  in    3,  once. 
3  in     6,  twice. 
3  in     9,  3  times. 
3  in  12,  4  times. 
3  in  15,  5  times. 


3  in  18,  6  times. 
3  in  21,  7  times. 
3  in  24,  8  times. 
3  in  27,  9  times. 
3  in  30,  10  times. 


DIVISION. 


LESSON    LXXVI. 

How  much  is  3  times  2  ? 

How  many  times  is  3  contained  in  6  ?   2  in  6  ? 

/\  1.  It  takes  three  lines  to  form  a 

triangle.      How  many  triangles  will 


twenty-one  lines  form  ? 

2.  How  many  cents  will  15  apples  cost,  at  the 
rate  of  3  for  a  cent  ? 

3.  If  we  walk  three  miles  an  hour,  how  many 
hours  will  it  take  us  to  walk  twelve  miles? 

4.~lf  3  pounds  of  butter  last  a  family  a  week, 
how  many  weeks  will  thirty  pounds  last  them  ? 

5.  Twenty-four  is  how  many  times  three  ? 

6.  How  much  is  half  of  18?     How  many 
times  3  is  9  ? 

One  half  of  18  is  how  many  times  3  ? 

7.  One  half  of  6  is  how  many  times  3  ? 

8.  If  it  takes  3  feet  to  make  a  yard,  how 
many  yards  are  there  in  27  feet  of  ribbon  ? 

9.  Thomas  divided  eighteen  almonds  equally 
among  his  three  sisters ;  how  many  did  he  give 
each  ?     How  often  will  6  go  into  18  ? 


4  in    4,  once. 
4  in     8,  twice. 
4  in  12,  3  times. 
4  in  16,  4  times. 
4  in  20,  5  times. 


4  in  24,  6  times. 

4  in  28,  7  times. 

4  in  32,  8  times. 

4  in  36,  9  times. 

4  in  40,  10  times. 


80  DIVISION. 


LESSON    LXXVII. 

Any  number  is  contained  in  0,  0  times. 

1  in  0,  0  times.     2  in  0,  0  times.     3  in  0, 
0  times,  &c. 

Divide  1208  by  4,  on  your  slate. 

Set  down  4,  the  number  you  divide 
by,  at  the  left  of  the  other  number 
with  a  line  between. 

In  dividing,  always  commence  at  the  left. 

As  you  find  the  quotient,  write  it  under  the 
number  divided  ? 

4  is  not  contained  in  1.     See,  then,  how  often 
it  will  go  into  12,  the  first  two  figures. 

4  in  12,  3  times.     Set  down  3  under  the  2. 

4  in  0,  0  times.     Set  it  down.  4)  1208 

4  in  8,  twice.     Set  down  2.  Ans.       302 

Do  these  sums  in  Division  on  your  slate : — 

(1)  (2)  (3)  (4)  (5) 

4)204    4)808   2)682   2^1020   3)  9630 

(6)  (7)  (8)  (9)  (10) 

1)768        2)168        3)186        3)2109        3)  3009 


5  in    5,  once. 
5  in  10,  twice. 
5  in  15,  3  times. 
5  in  20,  4  times. 
5  in  25,  5  times. 


5  in  30,     6  times. 

5  in  35,     7  times. 

5  in  40,     8  times. 

5  in  45,     9  times. 

5  in  50,  10  times. 


DIVISION.  81 


LESSON 

1.  If  four  wheels  are  needed  for  one  car,  how 
many  cars  will  twenty-eight  wheels  suj^ly  ? 

MODEL. — If  4  wheels  are  needed  for  one  car,  28  wheels 
will  supply  as  many  cars  as  4  is  contained  times  in  28,— or 
7  cars.  Answer,  7  cars. 

2.  A  farmer  distributes  40  pigs  equally  in 
four  pens.     How  many  does  he  put  in  each  ? 

3.  A  man  who  earns  4  dollars  a  week,  is  paid 
24  dollars.     For  how  many  weeks  is  he  paid  ? 

4.  If  I  place  four  boys  on  a  bench,  how  many 
benches  shall  I  need  for  thirty-six  boys  ? 

5.  If  5   oranges   are  worth   as  much  as  15 
apples,  how  many  apples  is  one  orange  worth  ? 

6.  If  five  rocking-horses  cost  forty-five  dollars, 
how  much  do  they  cost  apiece  ? 

7.  How  many  dresses  will  12  yards  of  ribbon 
trim,  if  it  takes  4  yards  to  trim  one  dress  ? 

8.  Four  pecks  make  a  bushel;    how  many 
bushels  will  16  pecks  make  ? 

9.  If  one  pew  holds  five  persons,  how  many 
pews  will  it  take  to  hold  thirty  persons? 


6  in    6,  once. 

6  in  12,  twice. 

6  in  18,  3  times. 

6  in  24,  4  times. 

6  in  30,  5  times. 


6  in  36,  6  times. 
6  in  42,  7  times. 
6  in  48,  8  times. 
6  in  54,  9  times. 
6  in  60,  10  times. 


82  DIVISION. 


LESSON    LXXIX. 

SUMS     FOR     THE     SLATE. 
*  t 

1.  Divide  twelve  hundred  by  4.     Divide  it 
by  6.     Divide  it  by  3. 

2.  Divide  two  thousand  five  hundred  and  five 
by  five. 

3.  Divide  four  thousand  eight  hundred  and 
sixty  by  six.     Divide  it  by  two. 

4.  How  many  times  is  five  contained  in  thirty- 
five  hundred  and  fifty-five  ? 

5.  How  many  times  is  six  contained  in  three 
thousand  six  hundred  and  six  ? 

6.  If  two  thousand  dollars  be  divided  equally 
among  five  persons,  how  much  will  each  get  ? 

7.  If   four  hundred  and  twenty  books  are 
distributed  equally  on   six  shelves,  how   many 
will  there  be  on  each  shelf? 

8.  If  four  hundred  soldiers  are  divided  into 
5  companies,  how  many  will  there  be  in  each  ? 

9.  If  four  partners  together  make  two  thou- 
sand dollars  in   one  year,  how  much  is   that 
apiece  ? 


7  in    7,  once. 

7  in  14,  twice. 

7  in  21,  3  times. 

7  in  28,  4  times. 

7  in  35,  5  times. 


7  in  42,  6  times. 
7  in  49,  7  times. 
7  in  56,  8  times. 
7  in  63,  9  times. 
7  in  70,  10  times. 


DIVISION.  83 


LESSON    LXXX. 

1.  Kuth  is  sent  to  divide  18  cakes  equally 
among  her  6  sisters.     How  many  must  she  give 
each? 

2.  How  many  classes  of  six  scholars  each  can 
be  formed  out  of  fifty-four  scholars  ? 

3.  Allowing  six  candles  to  the  pound,  how 
many  pounds  are  there  in  thirty- six  candles  ? 

4.  How  many  books  can  be  made  out  of  60 
sheets  of  paper,  if  it  takes  6  sheets  to  make  one 
book? 

5.  Paul  has  4  cents,  and  Kose  has  20.     They 
put  their  money  together,  and  divide  it  equally 
among  6  poor  girls.     How  much  does  each  girl 
get? 

6.  If  one  horse  can  draw  as  much  as  7  men, 
how  many  horses  will  draw  as  much  as  56  men  ? 

7.  How  many  weeks  of  7  days  each  are  there 
in  49  days  ? 

8.  I  am  63  years  old,  and  am  just  7  times  the 
age  of  my  son.     How  old  is  my  son  ? 

9.  Seven  times  two  is  how  many  times  seven  ? 


8  in     8,  once. 

8  in  16,  twice. 

8  in  24,  3  times. 

8  in  32,  4  times. 

8  in  40,  5  times. 


8  in  48,  6  times. 

8  in  56,  7  times. 

8  in  64,  8  times. 

8  in  72,  9  times. 

8  in  80,  10  times. 


84 


DIVISION. 


LESSON    LXXXI. 


These  eight  boys  are  having  a  fine  sail. 

If  they  are  charged  40  cents  for  the  boat,  how 
much  will  each  have  to  pay  ? 

If  they  catch  24  fish  and  divide  them  equally, 
how  many  will  each  get  ? 

If  they  have  16  apples  along,  how  many  will 
there  be  for  each  boy  ? 

How  many  times  eight  is  the  half  of  16  ? 


9  in     9,  once. 
9  in  18,  twice. 
9  in  27,  3  times. 
9  in  36,  4  times. 
9  in  45,  5  times. 


9  in  54,  6  times. 

9  in  63,  7  times. 

9  in  72,  8  times. 

9  in  81,  9  times. 

9  in  90,  10  times. 


DIVISION.  85 


LESSON    LXXXII. 
SUMS     FOE     THE     SLATE. 

1.  If  one  stage-coacli  will  hold  9  passengers, 
how  many  such   coaches   will   it  take   to   hold 
ninety-nine  passengers  ? 

2.  How  many  nine-gallon  jars  will  it  take  to 
hold  two  hundred  and  seventy  gallons? 

3.  If  a  family  use  nine  pounds  of  coffee  in  a 
month,  how  long  will  one  hundred  and  eighty- 
nine  pounds  last  them  ? 

4.  How  many  sets  of  9  volumes  each  can  be 
made  up  out  of  nine  thousand  and  ninety  volumes  ? 

5.  If  three  thousand  two  hundred  and  eight 
dollars  be  divided  among  eight  heirs,  how  many 
dollars  will  each  receive  ? 

6.  If  there  are  eight  panes  of  glass  in  one 
window,  how  many  windows    will  four  hundred 
and  eighty-eight  panes  supply  ? 

7.  Divide  eight  thousand  one  hundred  by  9. 
Write  down  the  even  tens  up  to  100 : — 10, 

20,  30,  &c. 


10  in  10,  once. 

10  in  20,  twice. 

10  in  30,  3  times. 

10  in  40,  4  times. 

10  in  50,  5  times. 


10  in  60,  6  times. 
10  in  70,  7  times. 
10  in"  80,  8  times. 
10  in  90,  9  tirnes. 
10  in  100,  10  times. 


SUMS    IN    DIVISION. 


LESSON   LXXXIII. 

What  is  Numeration  ?     What  is  Notation  ? 

What  is  Addition  ?     What  is  Subtraction  ? 

What  is  Multiplication  ?     What  is  Division  ? 

What  is  the  result,  or  answer,  called  in  Ad- 
dition? What  in  Subtraction?  What  in  Mul- 
tiplication ?  What  in  Division  ? 

1.  Ten  cents  make  a  dime.     How  many  dimes 
in  fifty  cents  ? 

2.  Ten  dimes  make   a  dollar.     How  many 
dollars  in  eighty  dimes  ? 

3.  Ten  dollars  make  an  eagle.     How  many 
eagles  in  thirty  dollars  ? 

4.  How  many  companies  of  ten  men  each  can 
be  formed  out  of  ninety  men  ? 

5.  Charles  has  7  dollars,  and  Robert  3.     They 
put  their  money  together,  and  buy  ten  turkeys. 
What  do  the  turkeys  cost  apiece  ? 

6.  A  man  riding  10  miles  an  hour,  travels  20 
miles.     How  many  hours  is  he  on  the  way  ? 

7.  If  ten  omnibus  tickets  cost  60  cents,  what 
does  one  ticket  cost  ? 

Do  the  following  sums  on  your  slate : 

(1)  (2)  (3)  (4) 

8)7208    9)  7290    9)  3699    10)  7000 


DIVISION.  87 


LESSON    LXXXIV. 

How  often  is  6  contained  in  7  ? 

Ans.  It  is  contained  once  •  for  6  in  6,  once. 

It  is  not  contained  twice  ;  for  twice  6  is  12. 

Is  6  contained  in  7  once  exactly  ? 

Ans.  No;  6  is  contained  once  exactly  in  6. 
As  7  is  one  more  than  6,  we  say  that  6  goes  into 
7  once,  and  one  over. 

How  often  is  6  contained  in  20  ? 
Ans.  6  in  18,  3  times ;  18  from  20  leaves  2. 
Hence  6  goes  into  20  three  times,  and  two  over. 

How  often  will  3  go  into  26  ?  4  into  38  ?  7 
into  50  ?  2  into  21  ?  8  into  55  ?  5  into  44  ? 

What  is  that  which  is  left  over  called  ? 
Ans.  The  Remainder. 

If  we  come  to  a  figure  too  small  to  contain 
the  one  we  are  dividing  by,  what  do  we  do  ? 

Ans.  If  it  is  not  the  first  figure,  we  set  down 
0  in  the  quotient. 

Divide  3604  by  6. 

6)  3604 

Quotient       600,  and  4  remainder. 

Divide,  as  above,  on  your  slate  :  (1.)  635  by  9. 
(2.)  563  by  8.  (3.)  4089  by  4.  (4.)  621  by  2. 
(5.)  6308  by  3.  (6.)  499  by  7.  (7.)  4009  by  5. 


88  CARRYING   IN   DIVISION. 


LESSON    LXXXV. 


3  2 


Look  at  this  sum.    Commence 
4)  3901  at  the  left.     4  is  not  contained  in 

975,  i  rem.        3.     See,  then,  how  often  it  will  go 

into  39,  the  first  two  figures. 
4  in  39,  9  times  and  3  over.     Set  down  9 
under  the  9,  and  prefix  the  remainder  3,  in  your 
mind,  to  the  next  figure — making  30. 

1  4  in  30,  7  times  and  2  over.  Set  down  7 
under  the  0,  and  prefix  2  to  the  next  figure- 
making  21. 

4  in  21,  5  times  and  1  over.  Set  down  5,  and 
the  remainder  1  to  the  right.  Answer :  quotient 
975,  and  1  remainder. 

This  prefixing  of  the  remainder  to  the  next 
figure  is  called  Carrying. 

When  must  we  carry  in  Division  ? 
Ans.  Whenever,  before  reaching  the  end  of 
the  sum,  we  have  a  remainder. 

Do  these  sums  aloud,  like  the  above  example  : 

(1)  (2)  (3) 

2)1349  3)2_904          4)JL762 

Quo.     674,  1  rein.  Quo.     968  Quo.     440,  2  rem. 

(4)  (5)  (6)  (7) 

5)  2564          6)  6702          8)  9679          9)4235 


DIVIDING   BY   TEN.  89 


LESSON    LXXXVI. 

Divide  4017  by  10.  10)4017 

10  in  40, 4  times.    Set  down 

A          J        4.1.     f\  401.  Trem. 

4  under  the  0. 

10  in  1,  0  times  and  1  over.  Set  down  0,  and 
carry  1.  10  in  17,  once  and  7  over.  Set  down 
1,  and  7  for  the  remainder.  Answer,  401  and 
7  remainder. 

Now  compare  this  answer  with  the  number 
to  be  divided — 4017.  It  is  the  same  as  if  we  had 
cut  off  the  right  hand  figure  for  the  remainder, 
and  taken  the  rest  for  the  quotient — 401 1 7. 

Give,  then,  an  easy  rule  for  dividing  by  10. 

Ans.  Cut  off  the  right-hand  figure  of  the 
number  to  be  divided  for  the  remainder,  and  take 
the  other  figures  for  the  quotient. 

Set  down  the  following  numbers.  Divide 
them  by  10  in  the  way  just  shown. 

1.  Five  thousand  two  hundred  and  nineteen. 

2.  Eighteen  hundred  and  sixty-three. 

3.  Nine  thousand  and  seventy-eight. 

4.  Eleven  hundred  and  eleven. 

5.  Four  thousand  one  hundred  and  forty. 

6.  Seven  thousand  two  hundred  and  six. 

7.  Nine  hundred  and  ninety-four. 

8.  Eight  thousand  and  one. 

9.  Nineteen  hundred  and  five. 


90  SUMS    IN   ADDITION. 

LESSON    LXXXVII. 

What  sign  is  used  to  denote  Addition  ? 
Ans.  This  sign  +  ,  called  plus, 

What  does  4  +  5  mean  ? 

Ans.  It  is  read,  four  plus  five.  It  means  4 
added  to  5,  and  is  equal  to  9. 

When  numbers  are  to  be  added  or  subtracted, 
how  must  we  be  sure  to  set  them  down  ? 

Ans.  So  as  to  bring  units  under  units,  tens 
under  tens,  &c. 

Eead  the  following  sums.  Set  down  the 
numbers  properly,  and  add  them  on  your  slate. 

1.  987  +  764-3665  +  544-2443.       Ans.  7225. 

2.  752  +  3953  +  414+6  +  1745.       Ans.  6870. 

3.  306  +  1032  +  89  +  567  +  765. 

4.  4  +  455  +  2260  +  1476  +  7+3488. 

5.  8  +  859  +  4954+483  +  1891  +  10  +  705. 

6.  10  +  758  +  655  +  950  +  62  +  969  +  863  +  737. 

7.  1659  +  2  +  2348  +  9  +  3299  + 1028  +  79  + 17. 

8.  1728  +  756  +  1699  +  789  +  1967+539  +  154. 
How  many  tens  must  we  add  together,  to  pro- 
duce 80  ?     Set  them  down,  and  add  them. 

How  many  one  hundreds  must  we  add,  in 
order  to  get  1000  ?  Set  them  down,  and  add 
them. 

What  is  the  sum  of  8  times  10,  and  10  times 
100? 


SUMS   IN    SUBTRACTION. 


91 


LESSON    LXXXVIII. 

What  sign  is  used  to  denote  Subtraction  ? 
Ans.  This  sign  — ,  called  minus. 

What  does  5  —  4  mean  ? 
Ans.  It  is  read  five  minus  four.    It  means  4 
subtracted  from  5,  and  is  equal  to  1. 

When  minus  is  used,  which  is  the  number  to 
be  subtracted  ? 

Ans.  The  one  that  stands  after  the  minus. 


Read  the  following. 

1.  1829  —     304. 

2.  4506  —  2702. 

3.  1234  —    899. 

4.  4108  —  1053. 

5.  2738  —  1374. 

6.  2345  —  1779. 

7.  2301  —    126. 

8.  6456  —  1679. 


Find  the  remainders. 

9.  3647  —  1753. 

10.  4567  —  2679. 

11.  7091  —  5132. 

12.  5678  —  1679. 

13.  9000  —  7889. 

14.  6789  —  3289. 

15.  7890  —  4719. 

16.  2006  —  1018. 


17.  Mr.  W.  has  2500  d9llars  in  one  bank,  and 
5000  in  another.     He  buys  a  house  for  6000  dol- 
lars.    If  he  draws  out  money  enough  to  pay  for 
it,  how  much  will  he  have  left  in  bank  ? 

18.  How  much  is  2500  +  5000  —  6000  ? 

19.  How  much  is  1422  +  2578  —  1510  ? 

20.  How  much  is  3761  +  5239  —  999? 


92                         SUMS   IN   MULTIPLICATION. 

LESSON 

LXXXIZ. 

What  sign  is  used  to 
Ans.  This  sign  x  . 

denote  Multiplication  ? 

"What  does  4x5  mean  ? 

Ans.  It  means/bw  multiplied  lyfive,  and  is 
equal  to  20. 

Which  is  greater,  4x5  or  5x4? 
What  is  an  easy  way  of  multiplying  by  10  ? 
What  easy  way  of  multiplying  by  100  ? 

What  is  the  number  to  be  multiplied  called  ? 
Ans.  The  Multiplicand, 

What  is  the  number 
Ans.  The  Multiplier. 

you  multiply  by  called  ? 

When  the  multiplier  contains  0,  how  were 
you  told  to  proceed  ? 

Head  the  following  sums.     Find  the  products. 

1.  1605   x     6. 

10.     62   x   100. 

2.  4198   x     2. 

11.  396   x     19. 

3.     973   x     9. 

12.     57   x     80. 

4.     861   x   10.' 

13.  403   x     17. 

5.  1284   x     7. 

14.  189   x     20. 

6.  1066   x     5. 

15.  148    x     63. 

7.     851   x     8. 

16.     82   x     95. 

8.  2396   x     4. 

17.     25   x   204. 

9.     271   x   36. 

18.     65    x     90. 

SUMS   IN"   DIVISION.                                     93 

LESSON    SO. 

What  sign  is  used  to 
Ans.  This  sign  -7-. 

denote  Division  ? 

What  does  14-7-7  mean  ? 

Ans.  It  means  fourteen  divided  £y  seven,  and 
is  equal  to  2. 

When   the  sign  for  division  stands  between 
two  numbers,  which  is  to  be  divided  ? 
Ans.  The  one  before  it  is  to  be  divided  by 
the  one  after  it. 

What  is  the  number 

to  be  divided  called  ? 

Ans.  The  Dividend. 

What  is  the  number 
Ans.  The  Divisor. 

you  divide  by  called  ? 

What  easy  rule  was  given  for  dividing  by  10  ? 

Eead  the  following  sums.     Find  the  quotient 
and  remainder. 

1.  8064  —     4. 

10.  4713  —     5. 

2.  9193  —     3. 

11.  6565  -     9. 

3.  2709  -     9. 

12.  3709  -     8. 

4.  4004  -     5. 

13.  2723  -     4. 

5.  7777  -    2. 

14.  3379  -     6. 

6.  1941  -  10. 

15.  6055  -     3. 

7.  1468  -     1. 

16.  7327  -     8. 

8.  2496  -     7. 

17.  5403  -     7. 

9.  5684  —     6. 

18.  2670  -  10. 

94  MISCELLANEOUS    ST7MS. 

LESSON    XCI. 
PROMISCUOUS   MENTAL   SUMS. 

1.  If  a  man  earns   15   dollars  a  week,  and 
spends  9,  how  much  will  he  save  in  4  weeks  ? 
How  much  iff.  6  weeks  ? 

First  find  how  much  he  will  save  in  1  week,  then  in  4. 

2.  Ellen  puts  aside  3  cents  every  day  for  the 
poor,  and  James  puts  aside  5  cents.    'How  much 
will  they  both  have  for  the  poor  in  a  week  ? 

3.  We  collect  10  dollars  for  the  poor  one  day, 
and  6  the  next.     If  we  divide  the  whole  among 
4  poor  families,  how  much  will  each  get  ? 

4.  Mary  reads  2  pages  every  morning,  and  7 
every  afternoon  ;  how  many  pages  does  she  read 
in  a  week  ? 

5.  If  10  peaches  fill  a  quart  measure,  how 
many  quart  measures  will  80  peaches  fill  ? 

6.  A  farmer  has  3  white  hens  and  4  black 
ones.     If  each  hen  hatches  4  chickens,  how  many 
chickens  will  the  farmer  have  ? 

7.  If  8  pounds  of  butter  are  used  out  of  a  jar 
that  contains  17,  how  many  pounds  will  remain  ? 

8.  If  7  pears  cost  21  cents,  how  much  is  that 
apiece  ?     What  will  10  such  pears  cost  ? 

9.  A  lawn  contains  19  trees ;  2  are  oaks,  7 
firs,  and  the  rest  elms.      How  many  elms  are 
there  ? 


HALVES,   THIRDS,   FOURTHS. 


95 


LESSON    XOII. 

When  a  thing  is  divided  into  2 
equal  parts,  what  is  each  part  called  ? 
Ans.  A  Half. 

How  many  halves  in  a  whole  pear  ?     Count 
and  see. 

When  a  thing  is  divided  into  3 
equal  parts,  what  is  each  part  called  ? 

Ana.  A  Third. 
How  many  thirds  in  a  whole  pear  ? 

When  a  thing  is  divided  into 
equal  parts,  what  is  each  part  called  ? 
Ans.  A  Fourth,  or  Quarter. 

How  many  fourths,  or  quarters,  in  a  whole 
pear  ?     Count  and  see. 

What  is  this  line  divided  into  ? 
What  is  this  line  divided  into  ? 
What  is  this  line  divided  into  ? 


Which  is  greater,  a  half,  a  third,  or  a  fourth  ? 
Look  at  the  lines  divided  above,  and  see. 


96  FRACTIONS. 


LESSON    XCIII. 


If  a  whole  is  divided  into  5  equal  parts,  each 
part  is  called  one  Fifth. 

If  a  whole  is  divided  into  6  equal  parts,  each 
part  is  called  one  Sixth. 

If  a  whole  is  divided  into  7  equal  parts,  each 
part  is  called  one  Seventh. 

If  a  whole  is  divided  into  8  equal  parts,  each 
part  is  called  one  Eighth. 
*      . 

If  a  whole  is  divided  into  9  equal  parts,  each 
part  is  called  one  Ninth. 

If  a  whole  is  divided  into  10  equal  parts,  each 
part  is  called  one  Tenth. 

What  are  such  equal  parts  of  a  whole  called  ? 
Ans.  Fractions. 

Learn  how  to  write  these  fractions : — 


One  half 
One  third 
One  fourth 


One  fifth  i 
One  sixth  | 
One  seventh  |. 


One  eighth 
One  ninth 
One  tenth 


FRACTIONS.  97 


LESSON    XCIV. 

Learn  this  table  : — 


2  halves,  one  whole. 

3  thirds,    one  whole. 

4  fourths,  one  whole. 

5  fifths,     one  whole. 


6  sixths,      one  whole. 

7  sevenths,  one  whole. 

8  eighths,    one  whole. 

9  ninths,     one  whole. 


10  tenths,  one  whole. 

Since  2  halves  make  a  whole,  to  find  one  half 
cut  the  whole  into  2  equal  parts. 

To  find  half  of  a  number,  divide  it  by  2. 


To  find  i,  divide  by  3. 
To  find  £,  divide  by  4. 
To  find  ],  divide  by  5. 
To  find  £,  divide  by  6. 


To  find  -i,  divide  by  7. 
To  find  J,  divide  by  8. 
To  find  i,  divide  by  9. 
To  find  TV,  divide  by  10. 


SUMS   FOE   THE   SLATE. 

1.  What  is  i  of  6184  ?     Of  298  ?     Of  336  ? 

2.  What  is  1  of  369  ?     Of  1482  ?     Of  1578  ? 

3.  Find  one  tenth  of  8970.     Of  2310.    Of  80. 
4.' What  is  1  of  2548?     Of  332?     Of  380? 

5.  Find  one  sixth  of  1812.     Of  924.     Of  342. 

6.  Find  j  of  2808.      Of  6534.     Of  4851. 

7.  Find  1  of  4060.     Of  3750.     Of  4005. 

8.  Take  |  of  1752.     Of  7008.     Of  3224. 

9.  Take  1  of  5810.     Of  3325.     Of  693. 

i 


98 


FEDERAL    MONEY. 


LESSON    SOV. 

Now  we  must  learn  about  money,  weights,  &c. 
money   of  the   United   States 


What  is 
called  ? 


the 


Ans.  Federal  Money. 


Cent 


TABLE   OF   FEDERAL   MONEY. 

10  mills  make  1  cent. 
10  cents,  1  dime. 

10  dimes,          1  dollar. 
1  eagle. 


Dime. 


Eagle. 

Besides  these,  we  have  other  coins : — 
fThe  three  cent  piece,  worth    3  cents. 

«    The  half-dime,  worth    5  cents. 

f>  ^ 

[g    The  quarter-dollar,      worth  25  cents. 

[The  half-dollar,  worth  50  cents. 

.  fThe  quarter-eagle,  worth    2|  dollars. 

'I  -1  The  half-eagle,        worth    5    dollars. 

°  (The  double  eagle,  worth  20    dollars. 


FEDERAL   MONEY.  99 

I 


LESSON    XCVI. 

What  mark  is  used  to  denote  dollars  ? 

Ans.  This  mark  $,  placed  lefore  the  number. 

Twenty  dollars  is  written  $20. 

Twenty  dollars,  six  cents,  is  written  $20.06 

Twenty  dollars,  thirteen  cents,  $20.13 

Twenty  dollars,  twelve  cents,  1  mill,  $20.121 

Twenty  dollars,  one  mill,  $20.001 

The  first  two  figures  after  the  period  denote 
cents.     The  third  figure  denotes  mills. 

$60.019  is  read  sixty  dollars,  one  cent,  9  mills. 
$4.502,  four  dollars,  fifty  cents,  two  mills. 

Read  and  add  the  following.     In  setting  them 
down,  let  the  periods  all  range  in  line. 

1.  $103.24  +  $47.91  +  $3008.008  +  $546.356. 

2.  $6000.009  4-  $652.88  +  $1267 + $987.765. 

3.  $800.81  +  $6793.054  +  $21.421 +$1896. 

4.  $9.428  +  $4200.919  +  $87.75  +  $365.56. 

5.  From  eighty-seven  dollars,  forty     $87.405 
cents,  five  mills,  take  ten  dollars,  ninety- 
one  cents.  Ans.  $ 

6.  From  nine  hundred  dollars,  take  thirty-two 
dollars,  seventy-three  cents,  five  mills. 

7.  From    fifty    dollars,   seventy    cents,    take 
nineteen  dollars,  one  cent,  six  mills. 


100  EXERCISES   IN   FEDERAL   MONEY. 

LESSON   XOVII. 

1.  A  lady  buys  7  pounds  of  meat  at  10  cents 
a  pound ;  how  much  must  she  give  for  it  ? 

If  she  hands  the  butcher  a  dollar  bill,  how 
much  change  must  he  give  her  ? 

2.  Robert  buys  a  slate  for  10  cents,  and  a 
book  for  40  cents.   He  gives  the  store-keeper  half 
a  dollar.     How  much  change  must  he  receive  ? 

3.  John  buys  half  of  a  six  cent  pie,  and  hands 
the  baker  a  dime.   How  much  change  will  he  get  ? 

4.  How  many  cents  make  a  dime  ?   How  many 
cents  are  5  dimes  worth  ?     9  dimes  ?     10  dimes  ? 

1  dollar? 

5.  How  many  dollars  make  an  eagle  ?     How 
many  eagles  in  40  dollars  ?     In  80  dollars  ? 

6.  How  many  dollars  is  a  half-eagle  worth  ? 

2  half-eagles  ?     5  half-eagles  ?     10  half-eagles  ? 

7.  How  many  half-dimes   are   equal   to   10 
cents  ?    To  30  cents  ?    To  60  cents  ?    To  a  dollar? 

8.  I  leave  home  with  an  eagle  in  my  pocket. 
I  spend  $4  in  market,  and  on  my  way  home  give 
10  beggars  a  dime  each.     How  much  have  I  left  ? 

9.  If  a  man  deposits  an  eagle  in  the  savings 
bank  every  week,  how  many  dollars  will  he  have 
there  in  ten  weeks  ? 

10.  How  many  dimes  in  one  eagle  ? 

11.  If  a  boy  gives  a  store-keeper  a  dollar,  and 
gets  25  cents  change,  how  much  has  he  spent  ? 


STERLING   MONEY. 


101 


LESSON    XCVIII. 


What  is  the  money  of  Great  Britain  called  ? 
Ans.  English  or  Sterling  Money. 

Sovereign. 

TABLE   OF   STEELING   MONEY. 

.  4  farthings  make  1  penny. 
12  pence,  1  shilling. 

20  shillings,  1  pound. 

21  shillings,  1  guinea. 
What  mark  is  used  to  denote  pounds  ? 

Ans.  This  mark  £,  placed  before  the  number. 

Wh.at  coin  represents  1  pound? 
Ans.  The  sovereign,  a  gold  coin. 

How  many  shillings  is  1  sovereign  worth? 
Ans.  Twenty  shillings. 

Which  is  worth  more,  a  sovereign  or  a  guinea  ? 

1.  How  many  farthings  in  1  penny  ?     In  8 
pence?    In  10  pence? 

2.  What  part  of  a  penny  is  a  farthing  ? 

3.  How  many  farthings  in  a  half-penny  ? 

4.  If  I  pay  9  shillings  for  a  map,  and  £1  for 
a  book,  which  costs  the  more  ?   How  much  more  ? 

5.  If  a  boy  who  has  £2  spends  half  of  it,  how 
many  shillings  has  he  left  ? 

6.  Five  beggars  received  8  farthings   each, 
How  many  pence  did  that  make  for  all  five  ? 


102 


LESSON    SCIX. 

TROY  WEIGHT. 

What  is  Troy  weight  used  in  weighing  ? 
Ans.  Gold,  silver,  and  precious  stones. 

TABLE. 

24  grains  make      1  pennyweight. 
20  pennyweights,  1  ounce. 
12  ounces,  1  pound. 


APOTHECARIES'  WEIGHT. 

By  whom  is  Apothecaries'  weight  used  ? 
Ans.  By  apothecaries,  in  mixing  medicines. 

TABLE. 
20  grains  make  1  scruple. 

3  scruples,         1  dram. 

8  drachms,        1  ounce. 
12  ounces,  1  pound. 

1.  A  person  who  has  a  pound  of  gold  dust,  sells 
4  ounces  of  it.     How  many  ounces  has  he  left  ? 

2.  How  many   spoons   weighing   10  penny- 
weights each  will  it  take  to  make  an  ounce  ? 

3.  How  many  powders  of  5  grains  each  can  a 
druggist  make  out  of  1  scruple  of  calomel  ? 

4.  How  many  drams       in  2  ounces  ?     In  8 
ounces  ?    In  11  ounces  ? 


AVOIRDUPOIS   WEIGHT.  103 

LESSON    C. 

AVOIRDUPOIS  WEIGHT. 

What  is  Avoirdupois  Weight  used  for  ? 
Ans.  For  weighing  the  metals   except  gold 
and  silver,  groceries,  and  all  coarse  goods. 

TABLE. 

16  drams  make          1  ounce. 
16  ounces,  1  pound. 

25  pounds,  1  quarter. 

4  quarters,  1  hundred-weight. 

20  hundred-weight,    1  ton. 


1.  How  many  cornucopias  holding  4  ounces 
each  can  be  filled  with  a  pound  of  candy  ? 

2.  How  many  pounds   in  a  quarter  ?     In  a 
hundred-weight  ?    In  20  hundred-weight  ?     In  a 
ton? 

3.  How  many  pounds  in  2  tons  of  coal  ? 

4.  Emma  weighs  just  half  as  much  as  Charles, 
and  he  weighs  80  pounds.      What  is  Emma's 
weight  ? 

5.  If  a  grocer  sells  two  boys  half  .  a  pound  of 
cheese  each,  how  many  ounces  is  that  in  all  ? 

6.  If  5  pounds  are  used  out  of  a  quarter  of 
flour,  how  many  pounds  are  left  ? 

7.  If   a  hundred-weight   of  pork  is  divided 
among  10  men,  how  many  pounds  will  each  have  ? 


104:  LONG   MEASURE. 


LESSON    01. 
LONG    MEASURE. 

For  what  is  Long  Measure  used  ? 

Ans.  For  measuring  length  and  distance. 

One  inch. 

Make  a  line  one  inch  long  on  your  slate. 

TABLE. 

12    inches  make  1  foot. 

3    feet,  1  yard. 

5 J  yards,  1  rod  or  pole. 

40    rods,  1  furlong. 

8    furlongs,         1  mile. 

1.  How  many  inches  long  is  a  yard-stick  ? 

2.  A  boy  who  has  to  walk  a  mile  to  town, 
has  gone  half  the  way.     How  many  furlongs  has 
he  yet  to  go  ? 

3.  A  tall  man  is  6  feet  high.     How  many 
yards  is  that  ? 

4.  Allowing  a  yard  to  each  step,  how  many 
feet  will  a  man  go  in  10  steps  ? 

5.  How  many  rods  in  a  furlong?     In  8  fur- 
longs?    In  a  mile? 

6.  About  how  many  inches  wide  is  this  page  ? 

7.  How  many  inches  in  a  quarter  of  a  yard  ? 


LIQUID   MEASURE.  105 


LESSON    Oil. 
LIQUID     MEASURE. 

For  what  is  Liquid  Measure  used  ? 
Ans.  For  measuring  liquids;    such  as  milk, 
oil,  vinegar,  molasses,  liquors,  &c. 

TABLE. 

4  gills  make  1  pint. 

2  pints,  1  quart. 

4  quarts,  1  gallon. 

31^  gallons,  1  barrel. 

2  barrels,  1  hogshead. 

2  hogsheads,  1  pipe. 

2  pipes,  1  tun. 


1.  A  tumbler  holds  about  half  a  pint ;  how 
many  tumblerfuls  in  a  quart  ? 

2.  How  many  pints  will  fill  a  quart  measure  ? 

3.  If  a  milkman  mixes  2  pints  of  water  with 
4  quarts  of  milk,  how  much  will  he  have  in  all  ? 

4.  Suppose  half  a  gallon  leaks  out  of  a  barrel 
of  oil ;  how  many  gallons  remain  in  it  ? 

5.  How  many  quart  pitchers  can  be  filled 
from  a  two-gallon  pail  ? 

6.  How  many  barrels  will  a  pipe  of  wine  fill  ? 

7.  If  I  have  8  quarts  of  cider,  and  give  half 
of  it  away,  how  many  gallons  have  I  left  ? 


106  DRY   MEASURE. 


LESSON   CHI. 
DRY   MEASURE. 

For  what  is  Dry  Measure  used  ? 
Ans.  For  measuring  fruit,  vegetables,  coal, 
salt,  grain,  &c. 

TABLE. 

2  pints  make  1  quart. 
8  quarts,  1  peek. 
4  pecks,  1  bushel. 

36  bushels,        1  chaldron. 

The  dry  quart  measure  is  of  wood ;  the  liquid 
quart  measure  is  of  tin. 

A  small  measure  contains  2  quarts. 


1.  A  man  bought  a  bushel  of  apples  ;  if  one 
peck  was  rotten,  how  many  pecks  were  good  ? 

2.  How  many  quarts  in  a  half  peck  ? 

3.  If  a  horse  eats  8  quarts  of  oats  a  day,  how 
long  will  it  take  him  to  eat  a  bushel  ? 

4.  If  a  pint  of  chestnuts  costs  6  cents,  what 
will  a  quart  cost  ? 

5.  If  5  girls  go  a  berrying,  and  each  girl  picks 
a  quart,  how  many  pints  will  they  have  in  all  ? 

6.  Which  are  cheaper,  potatoes  at  a  dollar  a 
bushel,  or  30  cents  a  peck  ? 

7.  What  is  a  peck  of  corn  worth,  at  80  cents 
a  bushel  ? 


TIME   MEASURE.  107 


LESSON    CIV. 

TIME   MEASURE. 

60  seconds  make  1  minute. 
60  minutes,  1  hour. 

24  hours,  1  day. 

7  days,  1  week. 

4  weeks,  1  lunar  month. 

13  lunar  naonths,  1  year. 

How  many  days  in  a  lunar  month  ? 
What  other  kind  of  months  is  there  ? 
Ans.  Calendar  months. 
Name  the  calendar  months  of  the  year  in  order, 
and  the  number  of  days  in  each.       / 


1st  month,  January,  31. 

2d   month,  February,  28. 

3d   month,  March,  31. 

4th  month,  April,  30. 

5th  month,  May,  31. 

6th  month,  June,  30. 


7th  mo.,  July,  31. 

8th  mo.,  August,  31. 

9th  mo.,  September,  30. 

10th  mo.,  October,  31. 

llth  mo.,  November,  30. 

12th  mo.,  December,  31. 


These  days  added  together  make  365  days  in 
the  year.  Every  fourth  year  is  a  Leap  Year ; 
then  February  has  29  days,  and  the  year  366. 

There  are  four  seasons  in  the  year : — 
SPRING,  consisting  of  March,  April,  May ; 
SUMMER,  June,  July,  August ; 
AUTUMN  or  FALL,^3eptember,  October,  November ; 
WINTER,  December,  January,  February. 


108  MISCELLANEOUS   TABLE. 

LESSON    CV. 

MISCELLANEOUS   TABLE. 

j  12  things  make   1  dozen. 

(  12  dozen,  1  gross. 

20  things,  1  score. 

(  24  sheets,  1  quire  of  paper. 

\  20  quires,  1  ream. 

56  pounds,  1  firkin  of  butter. 

100  pounds,  1  quintal  of  fish. 

196  pounds,  1  barrel  of  flour. 

200  pounds,  1  barrel  of  pork. 


"Which  weighs  more,  a  barrel  of  flour  or  a 
barrel  of  pork,  and  how  much  ? 

2.  If  a  man  lives  to  be  u  three  score  years  and 
ten,"  how  old  is  he  ? 

3.  A  box  of  pens  holds  a  gross ;  how  many 
dozen  in  a  box  ?     How  many  pens  in  a  box  ? 

4.  How  many  sheets  in  one  fourth  of  a  quire 
of  paper  ? 

5.  If  five  pounds  of  butter  are  taken  out  of  a 
full  firkin,  how  many  pounds  will  remain  ? 

6.  How  many  pounds  in  5  quintals  of  codfish  ? 

7.  "Which  month  is  the  shortest  in  the  year  ? 

8.  John  was  to  st.a^iii:tli^city  a  week.     He 
has  been  there  5  days ;  how  imucli  longer  is  he 
to  stay  ? 

£. 


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UNIVERSITY  OF  CALIFORNIA  LIBRARY 


• 


APPLETONS'  ARITHMETICAL   SERIES. 
JEty  Gr.    P.     QTT^OKEWBOS,    A. ML. 

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